Fifa's chief investigator made a surprise swoop this week on members of the executive committee who took part in the controversial bids for the 2018 and 2022 World Cup.
The members – including Fifa president Sepp Blatter – were unaware that US attorney Michael Garcia would be in Zurich waiting to interview them ahead of the executive committee meeting.
It is understood that Garcia, who heads the investigatory chamber of Fifa's ethics committee, completed all the interviews on Wednesday and Thursday. Only 12 of the 24 members who took part in the vote in December 2010, plus Blatter, are still in office.
Jérôme Champagne, who announced earlier this year that he wants to stand against Blatter for the Fifa presidency next year, said Garcia's investigation held the key to the future reputation of the World Cup.
Champagne said: "The process must go to the end. The World Cup must be unimpeachable, it must be untainted and it must be incorruptible.
"My position is the process led by Mr Michael Garcia must be completed and we should know what he has learned – we are talking about political influence, about collusion, about votes."
Garcia's interviews are not thought to be connected with a report this week that the FBI is investigating payments from a company owned by Qatari Mohamed Bin Hammam to fellow former Fifa member Jack Warner and his family. Both men left Fifa in disgrace following a 2011 corruption scandal.
Garcia has already interviewed officials who worked on a number of the bid teams, including England's unsuccessful 2018 campaign. It is unclear whether he has contacted the winning bid teams for Russia and Qatar so far.
A statement from Garcia's office said: "As with any investigation, the ethics committee does not comment on ongoing proceedings."