Vogue denies it. Ms Wintour offers up only her frozen 'Blue Steel' smile when asked. But the media are abuzz with rumours the daughter of Evening Standard Editor Charles Wintour is to become UK envoy.
The 63-year-old ice queen - nicknamed Anna "Nuclear" Wintour for her cool and aloof demeanor - may not be the obvious choice for President Obama's British ambassador. It is not as if the war on terrorism could be won if only Afghanistan were kitted out in Tom Ford ready-to-wear.
London-born Ms Wintour is undeniably uber-powerful in her own circles, however, and those circles include rubbing shoulders with New York celebrities who shell out $40,000-a-ticket for fundraising suppers. Ms Wintour and her air-kisses-best-mate Sarah Jessica Parker held one such fundraiser in New York in the summer and, in all, Ms Wintour reportedly raised more than $500,000 to re-elect the president.
Wintour: all business
But running a style bible and choosing pretty baubles is one thing. Running an embassy requires more than minimalist chic. Is the world ready for Ambassador Wintour - particularly in such a politically challenging posting as the UK, with Europe and the Middle East in economic and political turmoil?
Yes, argues Justin Kerr-Smiley, former press officer at the US Embassy in London and author of Under the Sun and several books of historical and political fiction.
"She's a business woman, isn't she, so why not?" Mr Kerr-Smiley said in an interview with Channel 4 News. "The Americans reward the faithful supporters and she's perfectly capable. There's a lot of protocol. Just because she's in fashion doesn't mean she isn't well read on contemporary issues."
Telegraph Diplomatic Correspondent Nile Gardiner was not entirely convinced, however, writing in his blog today entitled: "Anna Wnitour is a ludicrous pick for US Ambassador to London: the special relationship is not a fashion statement."
The tough jobs at the US embassy are often delegated to the Ambassador's deputy who is generally a career diplomat, however. So Ms Wintour may feel right at home in a palatial London residence giving orders to dozens of obliging staff in kitten heels.
The Devil Wore Prada
Ms Wintour has been a tour-de-force since she quit school in England at age 16 and headed for New York to make her mark in the city of dreams and tinsel hair extensions. Ms Wintour rose from Vogue creative director to editor-in-chief via an 18-month stint editing British Vogue. She has been at the magazine for 25 years and is believed to have been the inspiration behind the Meryl Streep film The Devil Wore Prada.
"I'm a very decision person. I think it is actually helpful to people that you are working with that you can make decisions so if Meryl seemed somewhat strong I respect that," Ms Wintour told Barbara Walters in a 2006 interview after the film opened.
Ms Wintour was at her diplomatic best last night in New York, refusing to comment on any possible government role when she stepped out for the premiere of new documentary about her Vogue work. Her publicist insists Ms Wintour is not interested.
"She has not been offered anything," Megan Salt told Channel 4 News today. "This is just a rumour and she is very happy at her current job."
Should President Obama be able to turn her head, however, Ms Wintour would not be the first celebrity ambassador. Child star Shirley Temple Black was appointed US ambassador to Ghana in 1974 and Czecholslovakia in 1989. Like Ms Wintour, Ms Black Temple was active in politics and not prepared to bow to public expectations and limit her career ambitions.
Ms Wintour admits she likes to get her own way.
"I try to give very clear direction to the people that I am working with and sometimes, unfortunately, they don't hear the answer they would like to hear," Ms Wintour said when she was interviewed by American talk show host David Letterman in 2009.
"I am not always warm and cuddly but I appreciate wonderful work, good work, creative talented people," she said.
"Have you ever put anybody in a headlock?" Mr Letterman asked in response.
"Maybe you," Ms Wintour replied, without missing a beat.