Fifa's vice president has told ITV News the "whole crux of the matter" is whether any of the payments allegedly made by Mohamed Bin Hammam "have a connection to Qatar's bid committee."
Football's world governing body faces fresh allegations over its decision to award the 2022 World Cup to Qatar.
Jim Boyce said: "Any evidence should be handed over to Michael Garcia and I await his report with great interest.
"He should be given full and complete control over his investigation. I'm not going to pre-judge his report."
Mr Boyce said he has "confidence" in Fifa's integrity, adding, "I have seen major reforms that have taken place since I started three years ago."
More top news
Sixties wildchild Marianne Faithfull has slammed pop stars Miley Cyrus and Rihanna as 'rubbishy sluts'.
High school player gives motivational post-match interview that is a cross between a sermon and an advert for the 'American dream'.
The first Pink Floyd album in more than 20 years, The Endless River, has been unveiled by the veteran rock band.