As part of China's campaign to be a sporting superpower, the city of Shanghai last year wrested the right to hold tennis's eight-player finale, known as the Tennis Masters, from Houston. Billboards and banners on the roadside leading from central Shanghai out to the 80-acre tennis complex in the suburb of Minhang showed images of the players, and proclaimed such slogans as "Friendship in Masters Cup, Passion in Minhang", like nonsensical fortune cookies.

On a cool morning last November, I set off for Minhang, so far from the city centre that it seemed like it was in another province, to watch the world's number one Roger Federer practise a few days before the Masters tournament started. But by then, the billboards were an unsettling reminder that three of the top eight had pulled out - Marat Safin and Andy Roddick because of injury and Lleyton Hewitt because his wife was expecting a baby. Worse than that, injury called into doubt Federer's participation as well. Just after making a special trip to Shanghai in early October to open the new Qi Zhong stadium, Federer injured his ankle practising at his home near the Swiss city of Basle. On crutches for two weeks, he had pulled out of three tournaments before the Masters and arrived in China short of match practice and stamina. His part-time coach, Tony Roche, who had not seen him since the summer when he won his third consecutive Wimbledon title, had arrived early to practise with him.

It was the second year in a row that Federer had won both Wimbledon and the US Open. No one has done that since the late 1930s when the American Don Budge stamped this double imprimatur of domination on the sport. Many former champions believe Federer could become the greatest tennis player ever. Over the next two weeks, the tennis world will have its eye on him at the Australian Open, the first event on the sport's four-tournament obstacle course on different surfaces, to see if the 24-year-old Swiss can clear the first hurdle towards winning all of them in the same year - the fabled Grand Slam.

Even though there were doubts that he was fit enough to play, Federer was chasing records yet again in Shanghai. He had lost just three matches all year and arrived in China seeking to emulate John McEnroe's commanding 1984 season tally of 82 wins and three losses.

Tennis stadiums, like theatres, lack magic when they are empty. At Qi Zhong that November morning, technicians kept testing the courtside electronic displays that alternately flashed "China Mobile" and "Shanghai Stock Exchange", a reminder that in the world's most frenetically capitalist economy, even play is work. Federer walked on for his one-hour session and warmly greeted his practice partner that morning, the Argentine David Nalbandian, the world number 11.

The only visible sign of Federer's injury as he headed for the baseline was a black ankle wrap that he would wear all week, but when he started trading balls with Nalbandian, his shots flew out of court as often as not. From the sidelines, Roche, dressed in a pink shirt and blue track suit bottoms and a baseball cap, made quiet suggestions. Federer's personal trainer, Pierre Paganini, who had been working on strengthening and stretching exercises in the weeks following the injury, watched with a worried look on his face. When Nalbandian and Federer started playing games in the second half-hour of their practice session, it was apparent that a mortal Federer had arrived in Shanghai.

If the world of tennis champions seems glamorous from afar, it did not feel that way in Shanghai. A semi-permanent cloud cover made the city look like the set for a Blade Runner sequel. The Hilton lobby, where the players were staying, had been taken over by the tournament sponsors: in one corner, a lurid green Heineken booth made a pretence at being a bar; in another, a silver Mercedes transformed part of the lobby into a car showroom. Crowds of autograph hunters swarmed outside and airport-style security greeted anyone entering the hotel.

Amid this bustle, I see Federer's girlfriend, Mirka Vavrinec, dressed in a yellow sweater and jeans, walking across the lobby with two friends, but there is no sign of Federer. He is caught in rush-hour traffic. "Sorry, I am waiting for him as well," she tells me. "It took one and a half hours to get back from the stadium yesterday. Maybe we have to organise a helicopter."

In the rarefied and ridiculously wealthy world of professional tennis, top players are usually contactable only through their management agents. Tournament rules require that they hold a press conference after every match they play, so it is understandable that most limit non-tournament press interviews to a minimum. But Vavrinec had confirmed the night before that she had arranged for me to meet Federer this evening. Close to 7pm, she sends a text: "Pls come up to Room 2024. Roger is here!"

Federer, in jeans and padding around without shoes on, lets me in to his suite. He looks thinner in person than the imposing figure he cuts on court. I joke that having endured the long commute to the stadium and back, I have shelved my plans to become a professional tennis player. He laughs and says that it is really not so bad. A giant fruit basket and a wine bucket are on the table between us. I begin by asking about the injury that has everyone in the tennis world in Shanghai pursing their lips. He says he is pleased with his recovery, but "I think about it a lot so I have to get that out of my system."

A few minutes later, he discovers I will be around for the whole tournament so there are likely to be other opportunities to interview Paganini, who I am scheduled to see that same evening. Federer wheels around and asks Vavrinec to cancel that interview and then sprawls across the couch in such a relaxed way that it looks as if he is preparing to chat all evening.

Throughout our meeting he is extraordinarily modest and natural - he sometimes seems almost as interested in the interviewer as I was in him.

I had read that Federer is training harder than he did before he became number one, so I ask why he feels the need to. "The funny thing is finally I've made the big breakthrough and I've become number one in the world and now people are asking me, 'Are you still interested in the game, are you still motivated?' Of course I am," he says. "This is where it starts really, where the dream comes true and then you can go two ways: you can say, 'OK I'm going to be a party animal' or you can say, 'I want more of this.' I decided to have more of it. It's very simple. I feel a great pride in being number one in the world and representing my sport, and that for me is more important than anything."

I ask how it happens that the public engagements of a tennis superstar came to be arranged by his girlfriend. "It just feels too complicated if you had to call somebody in London and then they had to call the hotel. This way, it's very simple. You call Mirka, Mirka asks me if it's OK. I say 'yes, that's OK' and everything is sorted out. Obviously, she's my girlfriend and if everything got too much, I would stop it right away." He says he usually stays in hotels the other players are not in so that he gets away from tennis when he is not on court. On occasion, childhood friends "help him" by joining him on tour; last year, one required extra time off from the bank he works at to do so.

Halfway through the interview, Roche drops by to see if Federer and Vavrinec would like to go out for dinner. Federer takes the opportunity to set up a time for me to speak with the coach the following day. It seems always to be this informal: a couple of days later, I am at work in the FT office in Shanghai when my mobile rings. The connection is bad and I think it is a squash partner in London scheduling a game. The caller rings again. It's actually Federer trying to arrange the interview I had asked for with his mother.

When I meet Lynette Federer, a brisk and energetic woman in her early fifties, she says that "when Roger could barely walk, he would kick the ball with me. He couldn't even see over the table-tennis table but he could hit the ball over the net. People kept saying 'he's amazing.'" Federer played squash with his father every Sunday, and soccer at school till he was 13. And he hit tennis balls - at cupboard doors, garage walls, anything really.

It seems his extraordinary hand-eye co-ordination was apparent very early on and was not the product of coaching. Although Lynette Federer coached children at the local club, she did not coach her son. He played at a tennis club where he was coached by an Australian, Peter Carter, who was a seminal influence on his game. "We had no plan A, no plan B. We had no intention of making him a professional tennis player," she says. Federer himself credits the range of sports he played as a child - he also played badminton and basketball - for his hand-eye co-ordination. "I was always very much more interested if a ball was involved," he says. Most tennis prodigies, by contrast, play tennis at the exclusion of pretty much everything else.

At the age of 14, Federer told a local tennis magazine he had decided to try to qualify for the Swiss national tennis centre in the French-speaking part of Switzerland. He hadn't told his parents of his decision. "This is quite a quote. It could change our lives," his mother recalls telling him when she read about it. The decision initially knocked Federer's happy childhood sideways. He spoke no French and had to live with a host family. The dislocating move away from his family coupled with the rigid discipline of the tennis centre completely sapped his confidence. He challenged the regimented drills of the coaches. In just a few months, Federer went from being a bubbly teenager to one who was withdrawn and lacked confidence. "He said, 'They seem to be saying I can't play tennis,'" Lynette Federer recalls emotionally, even a decade after the event. She and her husband, Robert, sought a meeting with the coaches and told them it was fine if their son trained hard but they didn't want his personality changed: "He is mischievous, but if you give a little, he will give you back so much," she says. The coaches eased off.

The easy-going star that we know today was not always so even-tempered. As a youngster, he would rage and burst into tears and fall apart in matches. His father would be so embarrassed that they would drive home in silence afterwards. But by the time he was beginning to be noticed on the world circuit in 2000, ranked 29, Federer had controlled his temper so well that he worried about not showing enough emotion on court. "Then I got too calm, too quiet and that was a problem." The next year, however, at 19, he beat seven-times Wimbledon champion Pete Sampras in the fourth round of the tournament (although he would have to wait another two years before winning it himself).

The following summer, his mentor, Peter Carter, was killed in a car accident on holiday in South Africa. Federer was devastated. By the summer of 2003, after crashing out of the French Open in the first round, Federer felt he was in danger of being written off. "People were starting to ask, 'Is this one of those talents who will never achieve something... who wasted his talents?' I was starting to feel the pressure from all sides," he recalls. After a sluggish start because of a bad back, he won Wimbledon that year, beating Australian Mark Philippoussis in straight sets. He fell back on the court and wept.

When it counts most, Federer seems able to lift his game to a metaphysical high that on the tennis circuit is known as being "in the zone". In last year's Wimbledon final he made number two seed Andy Roddick look flat-footed. At 5-5 in the second set Roddick punched a volley into open court and Federer, his arm like an aeroplane propeller, crashed a forehand past Roddick that prompted two-time Wimbledon champion Jimmy Connors to remark in the BBC commentary box that such shots "take my breath away - I can't comprehend it".

In his first match in the Shanghai Masters, Federer played patchily, coming back to win from 1-3 in the final set against Nalbandian. After the match a Chinese reporter asked nervously: "It is a rumour that you will quit the Masters Cup after the first [match] because of your injury. You won't quit, right?"

Federer didn't quit. But Rafael Nadal, who beat Federer on his way to a French Open victory in June, and the veteran Andre Agassi both pulled out because of injury the next day. The shell-shocked organisers held a hasty press conference, promising discounts the following year to make up for the mediocre field. Nadal went on court to apologise to the crowd. Later, when in the middle of his hard match with the Croatian Ivan Ljubicic, Federer called for a physiotherapist to help warm up his thigh muscles, you could feel the tension in the stadium. Federer eventually won 6-3, 2-6, 7-6.

That evening, a huddle of veteran tennis journalists had formed around the tournament director, Australian Brad Drewett, in the corridors leading to his offices. Drewett was recounting how Federer had made a special trip to Shanghai in early October to open the new stadium. What started as a request to be at the opening ceremony expanded into a 12-hour day of photo shoots, chats with sponsors and the press, and two sets of tennis with the former mayor of Shanghai as his partner. After a formal dinner with senior government officials, Federer asked Drewett if he and Vavrinec could go to the restaurant where the staff of the players' union and the tournament were having dinner so he could thank them personally. He stayed till 11pm.

The story prompted a reverential murmur from the tennis journalists. A few days later, Federer was asked about it by one of the British journalists: "A few of us who have been around for a few years can read off a list of people who would have said 'No way.' Why is it that you're the sort of guy who doesn't say no?" Federer's reply was matter of fact: "I knew I was here for the opening, not for myself. In the end, it was good fun. I don't get to spend every day with the government, especially from China."

In an era when tennis has been dominated by big serves and powerful groundstrokes, Federer has it all. Jim Courier, who won the French Open twice and was world number one in 1992, says: "I'm still looking for a shot he can't hit." What he lacks in miles per hour compared with the service of bionic men such as Roddick, he makes up for in placement. Federer credits Carter and a later coach, Peter Lundgren, with insisting he "go more for accuracy than power". That fabled hand-eye co-ordination allows his early racket preparation on the return to blunt the weapons of the game's big servers.

Federer's only relative weakness is his volley, in particular the drop volley. "As I kept improving from the baseline, I started to forget about going to the net," says Federer. "When Tony's around, he gives me advice on that. He volleys better than me... it's amazing to see how he does it. It's a very simple stroke and the more simple it is, the better it is."

It is the fluency with which he strikes the ball and the balletic grace with which he moves that have sportswriters searching for superlatives. One said seeing him play was like watching Michelangelo paint the Sistine Chapel. He never seems to be out of position and appears to be blessed with an internal positioning system that guides him to the ball.

Trainer Paganini pushes him to what he calls "endurance of explosivity" - the ability to play your best at 7-5 in the third when you have run the equivalent of three or four kilometres. One of the standard exercises is for Federer to mix sprints for a minute with playing for a couple of minutes. Another involves throwing medicine balls at a player crouching at a distance of 2m. "If you propose an exercise, he does it very quickly and sees more possibilities," Paganini says.

When Federer is not playing a tournament, the two work six to 10 times a week, and his appetite for training has increased dramatically in the past couple of years. "Last year his potential went up athletically," Paganini says. "He wanted to do everything in practice to be able to be even 1 per cent better."

Over the past two years the gap between Federer and the rest of the top players, with the exception of the Spanish teen prodigy Nadal, appears to have widened. He beat Hewitt in the 2004 US Open final by the embarrassing score of 6-0, 7-6, 6-0. Roddick acknowledged after being trounced in the Wimbledon final last year that he had run out of options because Federer had improved so much in the 12 months since Roddick lost to him at Wimbledon in 2004. The American, a baseliner, was forced to try to take to the net. "Once those players are [pushed] out of their comfort zone, they've got to come up with something different and if it's not quite their game, then you've already won a small victory before the ball has been hit," observes Roche, who compares Federer's all-court game and persona with Rod Laver. Laver won two Grand Slams in 1962 and 1969 and is widely regarded as the greatest player ever. "The beauty of Roger's game is that depending on what surface and what type of opponent he is playing, he has a lot of variation - you don't see that often in today's game," says Roche.

Purists may marvel when Federer is in full flow, but tennis's fortunes, like those of boxing, peak when there are great rivalries. Federer has served up some great routs, but routs don't do much for the sport's popularity - his demolition of Hewitt received the lowest ratings of a US Open final in decades - and he is not being challenged in the way John McEnroe tested Bjorn Borg or Martina Navratilova and Chris Evert pushed each other to new heights. Both those legendary rivalries were celebrated in nostalgic books last year, yet another indication that tennis's best days in the public eye are possibly in the past.

There is some hope of a great rivalry between Federer and Nadal. They are made for each other. Nadal is all brute power and chases everything down, while Federer has both power and finesse. "This makes it easier for the non-hardcore tennis fan to get involved," says Courier. "You are either for the man in black or the man in white." In Miami last year, when Nadal held a matchpoint against Federer and at the French Open when he beat him, it looked like the battle had been joined. Both won 11 titles each in 2005. "We all want to see Federer pushed to see how he responds at 5-5 in the fifth. That will draw the line in the sand between him and Sampras," says Courier.

In Shanghai in November, however, it was not to be. Nadal's injury and withdrawal prompted questions about whether his hard-charging style was taking a toll on his young body. Instead, Federer squared off against Nalbandian, who in spite of his loss to Federer in the first match, had won through to the knock-out stage and then into the final. The players came on court to Queen's "We will rock you" - an improvement on Neil Diamond's "Sweet Caroline" the day before - and an announcer rolling out every syllable of "Day-veed Naaal-bandeeeeean".

Federer was soon up two sets to love. Then, in a rerun of his performance earlier in the week, he appeared to run out of stamina and ideas. Nalbandian, who beat him in their first five encounters and is something of a bogeyman for the Swiss, moved him all around the court and out-hit him from the baseline. Despite an abundance of Swiss flags being brandished by Chinese supporters, the crowd seemed evenly split. Nalbandian fought back to two sets apiece, and suddenly the stadium reverberated with a roar of "Roger, Roger." Buoyed by that support, Federer rallied from 0-4 to pull ahead to 6-5 and 30-0. Then his normally spectacular serve misfired and the Argentine won the tiebreaker and the match.

Nalbandian looked as surprised as the crowd. It was Federer's first loss in 25 finals. Roche looked sombre. When the trophy was presented to Nalbandian, he began his acceptance speech by joking, "Roger, don't worry. You're going to win a lot of tournaments so let me keep this one."

Even if the quality of the play see-sawed, it was the kind of final - offering both a riveting contest and contrasting styles - that tennis fans routinely witnessed in the 1970s, 1980s and much of the 1990s. Chinese fans, the great new hope for tennis as for so many other industries, had risen to their feet, cheered lustily and taken sides.

I bumped into Richard Evans, a veteran journalist for Tennis Week, as I left the stadium. Federer simply didn't have the stamina today for a five-set match because of his injury-induced layoff, he said. I knew that in the early 1980s Evans had written a biography of John McEnroe, arguably the most naturally gifted tennis player ever. How did Federer measure up? "Federer has more natural ability than anyone - even Lew Hoad [the Australian great who nearly won the Grand Slam in 1956]," said Evans.

This week in Australia, Federer will again have to live with the lofty expectations that come with being routinely described as the kind of player we see once in a lifetime.