FIFA vice-president Jim Boyce would be in favour of re-running the vote for the 2022 World Cup if allegations that widespread corruption was involved in the Qatar bid were proven.
The Sunday Times has claimed that it had received "hundreds of millions" of documents which allegedly revealed that disgraced former FIFA executive committee member Mohamed Bin Hammam had made payments to football officials in return for votes for Qatar.
Boyce, who was not on the executive committee on the world governing body at the time of the vote, said FIFA's chief investigator Michael Garcia, who is already looking into allegations of corruption, would have to widen his investigation.
Boyce told Radio 5 Live's Sportsweek programme: "As a member currently of the FIFA executive committee, we feel that any evidence whatsoever that people involved were bribed to do a certain vote, all that evidence should go to Michael Garcia, whom FIFA have given full authority to, and let's await the report that comes back from Garcia.
"If Garcia's report comes up and his recommendations are that wrongdoing happened for that vote for the 2022 World Cup, I certainly as a member of the executive co 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 at that time, there's no doubt about that."
The Sunday Times alleged Bin Hammam, also the former Asian Football Confederation (AFC) president who was banned for life from football administration by the FIFA ethics committee, had 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.
Boyce, who said he had not had the chance to read the Sunday Times report, feels Garcia's investigation should not be hurried.
He said: "The man has got to be given full control to do that investigation thoroughly and if it takes more time to do that investigation thoroughly so be it.
"I have not met Garcia, but I'm told he's a man of the very, very highest calibre and I'm told he's someone who will not shirk the responsibilities that he has been given. I certainly hope that's going to be the situation."
Boyce pointed out that 50 per cent of the executive committee members at the time of the 2022 vote had since left the governing body.
The Northern Irishman also insisted FIFA president Sepp Blatter's position should not be called into question by the allegations.
He said: "From the day that I became a member of the executive committee and from the day that Sepp Blatter announced that he wanted to see complete and utter reforms carried out by FIFA, he has led these investigations and he has led a lot of the reforms that were badly needed at FIFA that are now being carried out.
"There is no suggestion whatsoever that he was involved in any wrongdoing.
"When Garcia's report comes back to him, as president of FIFA he has to give leadership.
"There are people in authority who are not aware of things that go on regarding other individuals and if he personally wasn't involved in this I don't think there's any reason whatsoever for him to resign.
"He is still the president of FIFA and I'm sure he, like the rest of the decent people and the people who are involved in FIFA, are awaiting with great interest Mr Garcia's report."
The Sunday Times said the official Qatar bid committee had always insisted Bin Hammam was an entirely separate individual who had nothing to do with the campaign to bring the World Cup to Doha.
But a senior politician called for a full and transparent investigation into how the 2022 World Cup was awarded to Qatar.
John Whittingdale, chairman of the Commons Culture, Media and Sport select committee, said on Sunday: "My committee examined allegations two years ago that there had been corrupt payments involved in the decision, and we called for a full, transparent investigation. However, since then, FIFA have attempted to brush off the allegations and not taken them anything like sufficiently seriously.
"If these revelations in the Sunday Times prove to be correct they are obviously extremely serious.
"There does need to be an urgent and full transparent investigation to establish the facts."
Whittingdale argued Blatter's position was "almost untenable" as he had been very dismissive of the allegations over the past couple of years and did not appear to have taken them seriously.
He added: "There have already been serious doubts raised about the capability of Qatar to host the 2022 World Cup on football grounds. If the choice of Qatar was as a result of improper payments being made, then that strengthens an already strong case for re-running the whole 2022 contest."
Gerry Sutcliffe was sports minister during the bidding process for the 2018 and 2022 World Cups, which were awarded simultaneously. England bid for the 2018 tournament, but lost out to Russia.
Sutcliffe cast doubt on whether a re-run of the 2022 bid would be possible, but said urgent action was required to show potential bidders for future tournaments it was still worthwhile funding a bid.
"It's called into question the whole integrity of FIFA," he said on Radio 5 Live.
"I think it would be difficult to re-run 2018 and 2022 now because the commitments have been made.
"What I think should happen is the FA, through UEFA, should make strong representations to FIFA, because what's going to happen is people are not going to bid in the future if it's not a fair and transparent process."