Jim Boyce has argued there should be a revote on the next two World Cups if it is proved the bidding process was corrupted.
Sepp Blatter announced earlier this month that he would stand down as Fifa president following a new election, just two days after winning re-election for a fifth term.
That followed the arrest of seven top Fifa officials in a massive FBI corruption probe.
And yesterday Fifa communications director Walter De Gregorio was sacked after sealing his own fate with a joke about the governing body on Swiss TV.
Gregorio told Swiss chat show Schawinski: "The Fifa president, secretary general and communications director are all travelling in a car. Who's driving? The police."
Fifa Secretary General Jerome Valcke said on Wednesday that Fifa would postpone the bidding process for the 2026 World Cup, as investigations continue into allegations that bribery helped determine the hosts of earlier competitions. Swiss authorities have opened a separate investigation into how the 2018 and 2022 World Cups were awarded to Russia and Qatar respectively.
Former Irish FA president Boyce, whose four-year reign as home nations vice president came to an end last month, said: "If there is undoubtedly proof that corruption was involved in the bids for both Russia and Qatar then I personally feel the executive committee and the new president, when he is elected, need to look at having a revote."
Yesterday, Fifa called an extraordinary executive committee meeting for July 20 when a new president will be elected.