Britain do not currently enter a team, fearing it would damage the independent status of the English, Welsh, Scottish and Northern Ireland teams.
But David Davies, the FA's executive director, is hoping to find a solution that will allow the host nation to compete in the 90,000-seat Wembley stadium, scheduled for completion in time for the 2006 World Cup.
Mr Davis, who represents English, Irish, Welsh and Northern Irish interests on the British Olympic Committee, said: "We will now look at how the home nations could take part in the football tournaments."
But the Scottish Football Association has reiterated its opposition to a GB football team. A spokeswoman said: "Our footballing identity is Scottish. We have discussed the idea of a British Olympic team in the past and turned it down. There was no interest."
Fifa president Sepp Blatter has expressed his delight at London's win.
"I am a happy man because football in England is very popular, is played at the highest level possible and they have all the stadia," Mr Blatter said.
The new Wembley Stadium's 436ft-high arch was lit up last night in celebration of London's successful 2012 bid.
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