Organisers of the 2022 World Cup in Qatar will meet Fifa investigator Michael Garcia on Monday amid growing calls for the Gulf state to be stripped of the right to hold the tournament.
The Sunday Times reported that payments of millions of pounds were made to officials who supported the bid.
Fifa vice-president Jim Boyce says he would support a re-vote if corruption allegations can be proven.
Qatar’s 2022 bid committee denies “all allegations of wrongdoing”.
New York lawyer Garcia, who is due to meet Qatari officials in Oman, is already conducting a long-running inquiry into the 2018 and 2022 World Cup bids.
The Sunday Times alleges football officials took a total of £3m in return for support of the Qatari bid.
Speaking on BBC Radio 5 live’s Sportsweek programme, Boyce said: “I certainly as a member of the executive committee would have absolutely no problem whatsoever if the recommendation was for a re-vote.
“If Garcia comes up with concrete evidence – and concrete evidence is given to the executive committee and to Fifa – then it has to be looked at very seriously.”
Former attorney general Lord Goldsmith, a member of Fifa’s independent committee on governance, backed Boyce’s stance.
“If it is proved that the decision to give Qatar the World Cup was procured by, frankly one can describe it no other way, bribery and improper influence, then that decision ought not to stand,” he told BBC Radio 4.
Mark Pieth, the law professor appointed by Fifa president Sepp Blatter to lead the independent committee on governance, agreed and called the latest revelations “exciting”.
In an interview with the BBC World Service’s Newsday programme, he also said he hoped The Sunday Times to share their information with Garcia.
Football Association chairman Greg Dyke has already said a new vote should take place if it was shown a “corrupt system” led to Qatar’s win, while UK Sports Minister Helen Grant said it was “essential that major sporting events are awarded in an open, fair and transparent manner”.
Allegations of corruption centre on former Fifa official Mohammed bin Hammam.
The Sunday Times claims to have obtained secret documents that implicate the former Asian Football Confederation president in corrupting members of football’s governing body to win the right to stage the 2022 World Cup.
The newspaper alleges the documents, seen by BBC sports editor David Bond, show that Bin Hammam, 65, was lobbying on his country’s behalf at least a year before the decision to award the country hosting rights.
They also allegedly show he had also made payments into accounts controlled by the presidents of 30 African football associations and accounts controlled by the Trinidadian Jack Warner, a former vice-president of Fifa.
Qatar’s bid committee and Bin Hammam have always strenuously denied any wrongdoing.
The bid committee has also rejected claims Bin Hammam actively lobbied on their behalf in the run-up to the vote in December 2010.
It added it was co-operating with Garcia, insisting it will “take whatever steps are necessary to defend the integrity of Qatar’s bid”.
Qatar defeated bids from South Korea, Japan, Australia and the United States to win the right to stage the 2022 World Cup.
Football Federation Australia said it may re-submit its bid to host the 2022 World Cup in the wake of the latest claims.
“It’s a serious development, they’re serious allegations and we’re looking to see what the response will be,” said FFA chief executive David Gallop.
He said the FFA had been involved in Fifa’s investigation into corruption and the 2010 vote that awarded the World Cup to Qatar.
“We’ve been heavily involved in this now for many months in terms of the investigation that Mr Garcia is carrying out,” said Gallop.
Nick Xenophon, an independent senator in Australia, argued that The Sunday Times revelations “raise again the suspicion that the Qatar bid was deeply flawed”.
In an interview with BBC Radio 5 live, he said there was “more than enough time to open the bidding process for the sake of the integrity of football and particular the integrity of Fifa”.
He added that the other unsuccessful bidders for the 2022 World Cup also had every right to feel aggrieved.