Confederation of African Football (Caf) president Issa Hayatou and executive committee member Jacques Anouma were reportedly paid US$1.5m by Qatar.
The accusations were made by British MPs at the culture, media and sport committee in the House of Commons.
MP Damian Collins said the evidence against the Fifa pair was submitted by the Sunday Times newspaper.
Collins said: “The Sunday Times’ submission, and this is to be published by us later, claims that 1.5million dollars was paid to Fifa executive committee members Issa Hayatou and Jacques Anouma who went on to vote for Qatar.”
Hayatou, a Cameroonian, has led Caf since 1988 while Ivory Coast’s Anouma has been on the confederation’s executive committee for the last four years.
The information submitted to British lawmakers also claimed that Qatar, who won the right to host the 2022 World Cup, employed an African fixer with close connections to Hayatou to arrange deals for votes.
“In Cairo, [former Fifa Secretary General Michel] Zen Ruffinen introduced the reporters to an acquaintance called Amadou Diallo,” read the statement.
“Zen Ruffinen claimed that Qatar was using Diallo to arrange financial deals with the African members in exchange for World Cup votes.
“Further inquiries established that Diallo had been employed by the Qatar bid and was also the “charge de mission” (chief assistant) to Issa Hayatou.”
The ethics committee of football’s world governing body last year banned Nigeria’s Amos Adamu and Tahiti’s Reynald Temarii after a Sunday Times investigation into World Cup bidding.
Adamu, who denies the claims, was banned for three years after he was caught seeking bribes from undercover reporters and has now taken his case to the Court of Arbitration for Sport.
The latest developments mean no fewer than eight executive committee members – one third of the total of 24 – have either been alleged to have been or already found guilty of impropriety in relation to the 2018 and 2022 World Cup bids.