Reports in the British media on Sunday claimed that former Asian Football Confederation (AFC) chief Mohammed bin Hammam paid up to $5 million to football officials in order to gain support for Qatar's bid.
Bin Hammam was formerly a member of FIFA's Executive Committee until being banned from all football activity for life in July 2013 amid allegations of bribery.
Qatar were awarded the tournament in December 2010, beating off competition from the United States, South Korea, Japan and Australia.
However, the bid has since been shrouded in controversy with doubts over players' ability to play in the Qatari summer heat expected to see the event moved to the winter months between November and January.
Several FIFA figures, including president Sepp Blatter, have admitted fault in overlooking the climate in Qatar as a potential problem.
Boyce has welcomed an investigation into the latest claims, putting faith in FIFA's chairman of the investigatory chamber of the Ethics Committee, former United States Attorney, Michael Garcia.
Boyce told BBC Radio 5 Live's 'Sportsweek': "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."
