Fifa vice-president Jim Boyce says he would support a re-vote to find a new host for the Qatar World Cup in 2022 if corruption allegations can be proven.
The Sunday Times alleges football officials took a total of £3m in return for support of the Qatari bid.
Qatar's 2022 bid committee has issued a statement reiterating that it denies "all allegations of wrongdoing".
Organisers are due to meet Fifa's ethics investigator Michael Garcia in Oman on Monday.
The New York lawyer is already conducting a long-running inquiry into the 2018 and 2022 World Cup bids.
Football Association chairman Greg Dyke also said a new vote should take place if it was shown a "corrupt system" had led to Qatar's win.
UK Sports Minister Helen Grant said it was "essential that major sporting events are awarded in an open, fair and transparent manner".
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.
"The Fifa executive committee are 100% behind Garcia," he continued. "He will be allowed to go and speak to anyone from around the world to complete his mission."
The allegations of corruption centre on former Fifa official Mohammed bin Hammam, with The Sunday Times claiming 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 2022 bid committee and Bin Hammam have always strenuously denied any wrongdoing and that he actively lobbied on their behalf in the run-up to the vote in December 2010.
When approached by The Sunday Times to respond to their fresh claims of obtaining secret documents, Bin Hammam's son Hamad Al Abdulla declined to comment on his behalf.
In a new statement issued on Sunday, the Qatar bid committee said it had "always upheld the highest standard of ethics and integrity in its successful bid to host the 2022 Fifa World Cup".
The committee said it was co-operating with Garcia's inquiry, adding: "We will take whatever steps are necessary to defend the integrity of Qatar's bid and our lawyers are looking into this matter.
"The right to host the tournament was won because it was the best bid and because it is time for the Middle East to host its first Fifa World Cup."
FA chairman Dyke backed Boyce and said the "serious allegations" had to be investigated, adding: "I think if it is shown it was a corrupt system and that the people who won used bribes and other influences to get the vote, then of course it has got to be done again."
Bin Hammam has previously been at the centre of controversy in the football world. He was initially banned from the sport for life in July 2011 after being found guilty of attempted bribery over votes in that year's Fifa presidential election.
However, his ban was annulled a year later by the Court of Arbitration for Sport, which said there was insufficient evidence to support the punishment.
Fifa issued him with a second life ban in December 2012 for "conflicts of interest" while he was president of the Asian Football Confederation.
In March 2014, The Daily Telegraph reported a company owned by Bin Hammam had paid Warner and his family more than £1m. Payments were claimed to have been made shortly after Qatar won the right to host the 2022 World Cup.
Qatar, which defeated bids from South Korea, Japan, Australia and the United States, has always insisted Bin Hammam never had any official role supporting their bid and always acted independently from the Qatar 2022 campaign.
Meanwhile, Shadow Secretary of State for International Development Jim Murphy told the BBC he had recently travelled to Qatar to investigate conditions of migrant employees working on World Cup infrastructure, amid accusations of abuse and deaths on building sites.
Almost 200 Nepalese men are reported to have died last year working on construction projects in Qatar.
Murphy said: "The revelations in today's Sunday Times, if proven, now call into question whether Qatar should hold the World Cup at all.
"There now needs to be a forensic inquiry into each and every one of those emails and documents to work out who paid what, when, for what, and what was the ebb and flow of votes and voting allegiances as a consequence.
"If that's proven, then the building work in Qatar has to stop, the vote has to be re-run, it has to be free and fair, because football fans deserve that."
Murphy added: "If Fifa doesn't act, it's lost the right to lead the world of football. Let's hope Qatar won fair and square, but there has to be an investigation."