The BBC's Panorama programme, which also accuses another FIFA executive of planning the corrupt sale of 2010 World Cup tickets, offered what it said was new evidence over the ruling body's appointment of International Sports and Leisure (ISL) as its marketing arm. ISL went bankrupt in 2001.
The programme said members Ricardo Teixeira of Brazil, hosts of the next World Cup, Confederation of African Football (CAF) chief Issa Hayatou and South American (CONMEBOL) head Nicolas Leoz took bribes from ISL to win the lucrative contract.
The trio are current members of the FIFA executive committee (ex-co) which will decide on Thursday which countries host the World Cups of 2018 and 2022.
All have denied any wrongdoing but neither they nor FIFA were available on Monday for comment on the latest allegations based on what the BBC said was a confidential ISL document which detailed 175 secret payments between 1989 and 1999.
Similar allegations were first made against them in a book by the presenter of Monday's programme, British investigative reporter Andrew Jennings.
FIFA President Sepp Blatter said in a statement issued by the BBC on Monday that no FIFA officials had been accused of any criminal offence during a 2008 inquiry and court hearing into the ISL collapse by Swiss authorities.
Blatter has recently criticised British media entrapment in claiming corruption within his organisation, although two members were suspended earlier this month following allegations of wrongdoing made by the Sunday Times.
A fourth member of FIFA's ex-co, Jack Warner of Trinidad who is a vice-president, had attempted to break FIFA rules over the sale of 2010 World Cup tickets "but the deal subsequently fell through", according to the Panorama programme.
Andy Anson, the head of the English bid to stage the 2018 World Cup, said earlier on Monday in Zurich that he feared the new Panorama allegations would damage their chances.
"Of course I'm disappointed with the timing and it's certainly not going to win any votes," Anson told reporters.
"We just have to see what happens tonight and move on. I won't be watching it, I've got other things to do."
England is bidding to stage the finals, for the second time, in 2018 against Russia, Spain and Portugal (one bid) and the Netherlands and Belgium (one bid).
FIFA will announce the winners, plus the hosts of the 2022 tournament, on Thursday at its headquarters in Zurich.
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