Mohammed bin Hammam, the former president of the Asian Football Confederation, is accused of masterminding the Qatari bid, and showering gifts and money on soccer officials around the world. He has been accused of channelling tens of thousands of dollars to the presidents of small football associations in Africa over several years.
Many of the payments were made shortly before the Fifa vote in 2010, leading some to claim that executive committee members could have felt pressured into voting for Qatar.
Along with the payments of thousands of dollars, soccer officials received all-expenses-paid trips to top hotels and gifts including cars.
Senior figures in soccer and politics lined up to condemn Fifa's management of the tournament, which opens in Brazil next week.
Boyce said any evidence of bribery should be given to Michael Garcia, a US lawyer appointed by Fifa to investigate the World Cup bidding process.
"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 [committee] would have absolutely no problem whatsoever if the recommendation was for a revote," said Boyce.
"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 decision to award Qatar the World Cup has been mired in controversy, with serious concerns about its ability to host the tournament.
The Telegraph has previously disclosed that a senior Fifa official and his family were paid almost US$2million ($2.3 million) from a Qatari firm controlled by bin Hammam shortly after the decision to award the tournament to the country.
The Qatar 2022 Bid Committee said it had always upheld the highest standard of ethics and integrity in its successful bid to host the World Cup.
"In regard to the latest allegations from the Sunday Times, we say again that Mohammed bin Hammam played no official or unofficial role in Qatar's 2022 Bid Committee."
It said it was co-operating fully with the Garcia investigation and remained totally confident that any objective inquiry would conclude it won the bid to host the World Cup fairly.