It would have been a diplomatic appointment that turned as many heads as a Vogue cover girl.
But as the president's second inauguration this weekend attracts to Washington an influx of celebrities who would normally be more at home in a fashion party than a political one, reports indicated that Miss Wintour is going to lose out on the most coveted US foreign service posting.
The president has instead decided to offer the ambassadorship to Matthew Barzun, who headed his formidable money machine as national finance chairman for the Obama re-election campaign, it emerged yesterday according to reports in the New York Times.
The two rival candidates for the post could not have more different backgrounds. Mr Barzun is a genial 52-year-old from Kentucky who made his money from a Californian tech media website and served from 2009 to 2011 as Mr Obama's ambassador in the rather less high-profile posting to Sweden.
Miss Wintour, 63, British-born but now a US citizen, has reigned over US Vogue since 1988. The icy demeanour that earned her the soubriquet of Nuclear Wintour was famously portrayed by Meryl Streep in the film The Devil Wears Prada .
What they both had in common was their prodigious fund-raising for Team Obama. A long-time Democrat supporter, Miss Wintour helped channel more than $500,000 towards the president's re-election campaign, including co-hosting a $40,000-a-plate dinner in Manhattan with the actress Sarah Jessica Parker.
Miss Wintour also has also developed a strong friendship with the Obamas since putting the new first lady on the cover of Vogue in Feb 2009 and is a regular visitor to the White House.
It was at a celebratory dinner of chicken and pumpkin pie hosted by Mr Obama for dozens of his top donors in late November that Miss Wintour reportedly made clear her interest in the London ambassadorship, which comes with an elegant residence on 12 acres of prime land in Regent's Park.
Also on her radar was the position in Paris where the ambassador resides in a mansion on the famed Rue du Faubourg Saint-Honore. Her interest in that position was yesterday said to have waned and hedge fund executive Marc Lasry is now favourite for the post.
Some 30 per cent of US ambassadors are political appointees and it has long been a tradition for the most prestigious posts to be awarded to major donors. Louis Susman, the current ambassador to London, is a Chicago financier who played a key role in raising funds for Mr Obama in 2008.
They also need deep pockets to do the job as the embassy budget comes nowhere near the costs of entertaining - a possible challenge for Miss Wintour.
Mr Barzun, who is organising this weekend's celebrations in Washington as co-chairman of the 2013 presidential inaugural committee, is reported to have been told that the London post is his if he wants it.
A Vogue spokesman insisted that Miss Wintour was very happy in her current job.
By Phillip Sherwell, Telegraph.co.uk