Paris bid leader Philippe Baudillon has warned people not to assume the 2012 Olympic vote is a straight fight between his city and London.
Many observers believe Wednesday's vote will be decided in a final-round face-off between Paris and London.
But Baudillon told BBC Sport: "The way the voting's organised is dangerous for each city. There is no front-runner.
"All of the cities can go far, but nobody knows which one, and each of the five can go out in the first round."
The secret ballot of International Olympic Committee members will proceed round by round until one city has an absolute majority, with the one with the least votes dropping out each time.
In an interview with this website, Baudillon echoed the view of London bid leader Lord Coe that it will be impossible to predict the final outcome until IOC president Jacques Rogge reads out the name of the winner.
"You have five big cities. Who knows who people will vote for in the first, second, third and perhaps the fourth round? Nobody knows," he said.
"I don't see my job as trying to bet on who is going to be here or there.
"My job is to try to convince a majority of IOC members that we are the best partner, have the best project and have the best commitment of everybody.
"We want to be very, very concentrated and committed until the last second and we need all the votes we can have in each round, especially the first round.
"It's a competition, and we have to be the best at each step of the competition."
Paris appeared to cement its status as front-runner for 2012 when it received a glowing evaluation report from IOC inspectors last month.
Baudillon believes IOC members will appreciate the fact the city is bidding for the third time in 20 years, and that it has key venues like its Olympic stadium already in place.
But because the ballot is secret, he knows members can vote without having to justify their choices.
The picture has been further clouded by reports that London and Madrid have been discussing a deal to get their supporters to switch allegiance to the other city if one of them is eliminated.
"When there is a competition like this, you have a lot of rumours and a lot of people who think they know. I've never heard about that and anyway we don't work like that," said Baudillon.
"We want to be very convincing and explain to each IOC member one by one why we're bidding and why we want the Games, so we cannot imagine this kind of process.
"We are here to win, but when you are in a competition you take the risk that you might not. But we are here to win."
The Singapore vote has also been billed as a showdown between British Prime Minister Tony Blair and French President Jacques Chirac.
Blair cannot stay for London's final presentation and the vote on Wednesday as he must return to the UK to host the G8 summit.
But Chirac will play a key role in the Paris presentation, delaying his arrival at the G8 in Scotland until the very last minute.
"[His presence in Singapore] is very important because it's a symbol of the commitment of Paris and France to the bidding process," said Baudillon.
"He was the head of the first bid 20 years ago. He knows the Olympic movement well and is very fond of it.
"He has met a lot of IOC members, when bidding and not bidding, because some of them are very close to him and to sport and he's very fond of sport.
"It's a long-lasting relationship between our president and the Olympic movement."