The Spanish capital is thought to have swung votes its way for the first round of the voting on Wednesday, thanks to lobbying from the former International Olympic Committee (IOC) president, Juan Antonio Samaranch, who has strong contacts with current members of the committee.
One city will drop out in each round until a city wins more than half the votes.
Paris and London are still thought to be leading the race, which is the subject of frantic last-minute jockeying between the contenders.
Tony Blair arrived in Singapore yesterday at the start of a two-day mission to convince the 117th IOC meeting to bring the games to London. Officials said Mr Blair would try to reassure the Olympic movement - part of which is still wary of troubled projects such as Wembley and Pickett's Lock, which was not ready in time to host the 2005 athletics world championships - that London's bid had the Government's full backing.
Mr Blair will complete his lobbying at the opening ceremony on Tuesday before flying back to host the G8 summit at Gleneagles, where he will be when the winner is announced shortly before 1pm Wednesday.
"What you get here in the last few days is a fantastic concentration of people and that's why the Prime Minister will be meeting a number of delegates which would not be possible otherwise" said Richard Caborn, the Sports minister.
Tessa Jowell, the Secretary of State for Sport said that "the momentum" was with London. She hinted, in an interview with The Independent, that London was within reach of beating the front runner, Paris, saying: "If Olympic votes are famous for anything, they are famous for surprises."
The imminence of the vote has helped to crystallise the thoughts of the 116 members who may now be more ready to declare their intentions in private.
Madrid's bid is gaining momentum. Its technical merits were confirmed in the IOC's evaluation report last month and Mr Samaranch is wielding considerable influence. "He has been active recently and still holds huge sway over members because he knows where the bodies are buried" said one source close to the bidding process.
Onedanger is that history may repeat itself, with one of the unfancied cities garnering a surprise sympathy vote and eliminating London or, less likely, Paris in the first round. Moscow, rated by bookies as a rank outsider, may not win but as it also has the support of Mr Samaranch, a former Spanish ambassador in the Russian capital, it could spring an early surprise.
Bid strategists reckon around 25 votes are needed to survive the first round. London hopes to have reached that mark with votes from Australia, New Zealand, South Africa, Canada, Malaysia and Singapore.
The London bid team rejected suggestions by the French media that it had been arrogant in assuming it had made the best progress in the past year. "I've heard the accusations of arrogance but its not arrogant in any way" said Craig Reedie, the head of the British Olympic Association. "This is a race to be won - you need 50 per cent plus one vote - and if you ask politely you may not get them."Reuse content