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
If your instinct is to be appalled – a careful consideration of the facts might just change your mind.
Russia is holding a briefing at the OPCW with Syrians from Douma, who, they promise, will say they were not victims of a chemical attack.
Ministry of Justice figures reveal assaults and self-harm behind bars climbed again last year to hit record highs.