On Tuesday, a British parliamentary inquiry into why England failed to secure the 2018 finals was told by member of parliament Damian Collins there was evidence from the Sunday Times newspaper that Issa Hayatou of Cameroon and Jacques Anouma of the Ivory Coast were paid by Qatar.
Both men have not commented.
"We categorically deny these allegations," Qatar, which defied the odds to win the vote to host the 2022 finals, said in a statement.
"We have nothing to hide and are prepared to support and cooperate with any further investigations and will be happy to counter any allegations from whistleblowers with real evidence."
Two other executive committee members, Nigerian Amos Adamu and Reynauld Temarii of Tahiti, were banned by FIFA's Ethics Committee last year after a previous Sunday Times investigation into the World Cup bidding process.
"The Qatar 2022 bid team ran an historic campaign that changed football. We were beset by rumours and allegations from the outset," the Qatar statement added.
"Bidding, like football, is a rough sport. Happily, our promise of bringing football to new lands and expanding its legacies across the developing world compelled FIFA."
At the same UK parliamentary inquiry, former English Football Association chairman David Triesman accused FIFA executive committee members Jack Warner, Ricardo Teixeira, Nicolas Leoz and Worawi Makudi of asking for favours in return for their votes for England's 2018 World Cup bid.
UK Sports Minister Hugh Robertson hinted to BBC radio on Wednesday that national associations may consider breaking away from FIFA if the world governing body does not act on the stream of allegations.
"I have taken the temperature from other football associations around the world. At the moment... there is a desire to try and work to change FIFA from the inside," he said.
"If FIFA proves unable to do that I would say that all options are possible."
Robertson said he hoped FIFA would look to root out possible corruption like the International Olympic Committee had after the 2002 Salt Lake City Winter Games vote scandal.
