We were at the Royal Academy for a dinner honouring the gregarious Mancunian collector Frank Cohen. Charles Saumarez Smith, the academy's incoming director, was the serene centre of a swirl of art-world players, among them the RA's exhibitions secretary Sir Norman Rosenthal, the artists Tracey Emin, Gavin Turk and Mat Collishaw, and the honoree, Frank Cohen.

Saumarez Smith, until recently the director of the National Gallery, was eloquent on the subject of his farewell party there. Upon the subject of his successor at the gallery, though, he was diplomatically mute. Nobody was indiscreet enough to mention the resignation three days before of the chairman of the gallery's trustees, Peter Scott, QC, whose alleged tactics of "bullying and undermining" had, according to some press reports, been the principal motor of Saumarez Smith's resignation in March.

Scott, who has been chairman of the Takeover Panel since 2000, will leave the gallery next August. Two other trustees, Mark Getty and Jon Snow, the Channel 4 newsreader, will also be leaving next year.

The National Gallery advertised for Saumarez Smith's successor in June, and retained the headhunters Saxton Bampfylde Hever. The trustees set up a selection committee of five of their number: Simon Burke, former chairman of Hamleys; Mark Getty, son of John Paul Getty Jr, the billionaire oilman who founded the Getty Museum; James Fenton, poet and art critic; Lady Normanby, author and literary critic; and the art historian Professor David Ekserdjian.

They are backed up by three advisers: Jennifer Montagu, an honorary fellow of the Warburg Institute; Alastair Laing, the curator of pictures and sculpture at the National Trust; and John Leighton, director general of the National Galleries of Scotland, an old National Gallery hand who was himself on the shortlist for the directorship on the last go-round.

The choice of a director has never been so fraught. The National Gallery is facing its worst crisis in a century with an acquisition budget capped at £40m this year and with a hog-wild market sucking long-term loans, currently valued at £200m, right off the walls.

So, ideally, the new director should combine the art-historical scholarship of Kenneth Clark, the diplomacy of Talleyrand and the messianic self-belief of L Ron Hubbard. Indeed, at times like these, the museum world, like the art market generally, takes on a distinct resemblance to the arena of Premiership football.

As is the way in these matters, lists of the names under discussion have bobbed to the surface. The longlist included Susan Foister, a Holbein expert who is the gallery's current director of collections.

Also on the list was Alexander "Sandy" Nairne, who had a long working relationship with Nicholas Serota at the Tate.

Nairne did much of the heavy lifting in the creation of Tate Modern and the re-creation of the Millbank gallery as Tate Britain, so it surprised some when he left the Tates to head up the National Portrait Gallery in 2002. Nairne himself says: "I am neither an applicant nor a candidate."

Others on the longer list include Malcolm Rogers, a Briton who has been director of the Boston Museum of Fine Arts since 1994. In his time there, Rogers has had experience of another typical museum-old furore when he fired two curators and merged several departments, provoking confrontations with important donors. Also on the list is Stephen Deuchar, the director of Tate Britain, who is widely judged ready to run his own show.

Finally, there has been some speculation that an American might be tapped. Of this suggestion, Jonathan Conlin, author of The Nation's Mantelpiece: A History of the National Gallery, observes that the last American to be suggested for the job was, in 1987 - Edward Pillsbury, the director of the Kimbell Art Museum, a jewel of a museum in Fort Worth, Texas.

While Neil MacGregor, the eventual appointee, had no previous museum experience, in the event he proved a strong and capable director. He moved on to direct the British Museum in 2002 and was replaced by Saumarez Smith.

And now?

It had been hoped that the selection committee would come up with a name by the end of September. "They've taken much longer than they should have done," says Richard Shone, editor of The Burlington Magazine. It is said that the committee is deadlocked.

The shortlist is rumoured to consist of three names. One, Nicholas Penny, is much favoured by the old-school curators, being a distinguished scholar and for 12 years a curator at the National Gallery.

Clearly, this is a time when gladhanding donors and lenders has become more important than ever. This is an area in which Penny, who is now senior curator of sculpture at the National Gallery of Art, Washington, DC, is something of an unknown quantity. And, doubtless, this will be on the minds of several members of the selection committee.

A second name is that of Gabriele Finaldi, also a former curator at the National Gallery, who left to become deputy director of the Prado. Finaldi, who is both a scholar and possessed of formidable negotiating skills, certainly did his cause no damage by playing a major part in putting together an exhibition that many thought could never happen, the National Gallery's blockbuster Velázquez show last summer.

His own Velázquez show, a triumphal quid pro quo, opens at the Prado shortly.

And the third candidate?

The front-runner is said to be Axel Ruger, another former National Gallery curator, who has been director of the Van Gogh Museum in Amsterdam since the beginning of last year. Ruger is skilled at dealing with media and patrons.

So we shall see. After the committee have agreed on a candidate, the name will go up to the entire board of trustees. If approved, it then goes to the prime minister's office for rubber-stamping.

The name might well, of course, be one of those on the long list. Or there might be a surprise.

Henry Kissinger was once asked why intrigues in academia are so bitter. He famously answered: "Because the stakes are so low."

At the National Gallery right now, though the stakes are very high indeed, perhaps the intrigues will be put on hold.

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