Beckham sent 91,000 spectators into a frenzy at Beijing's National Stadium when he appeared from within a red London bus at Sunday's closing ceremony. He revealed that he could coach an all-star Great Britain football team at the 2012 games, with his old Manchester United boss Sir Alex Ferguson as manager. "We deserve to have a football Team GB at the Olympics and I hope it gets sorted," said LA Galaxy midfielder Beckham.
Beckham will be 37 in 2012 and said it is unlikely that he will play. But asked if he would take a key role, he said: "I think it's possible."
Olympic hero Lord Coe, head of the 2012 organisers, has already asked Ferguson to manage the side, The Sun reported.
Britain has been barred from Olympic football because England, Scotland, Wales and Northern Ireland compete separately in international matches.
But Prime Minister Gordon Brown is determined to resolve the issue and has held talks with football's governing body FIFA.
On Sunday, Portsmouth manager Harry Redknapp admitted that he would love the job.
He said: "Would I take it if they offered it to me? Absolutely - I'd be a fool not to. The biggest problem I'd have is who to leave out."
Mayor Boris Johnson will fly the Olympic flag at City Hall after he returns on Tuesday. The Mayor said he was "humbled" by the honour of receiving the banner.