Gerhard Mayer-Vorfelder, the former German FA (DFB) chief was a highly influential Executive Committee member until 2007 and is still a member of FIFA's Players Status Committee.
Although he will not have a vote on December 2 when the destination of the World Cups is decided, he said it could be tricky to go ahead with a decision then until an investigation sheds full light on the affair.
"The awarding (of the World Cups) should be postponed until the question is cleared up, in a negative or a positive way," he told Sport Bild magazine.
"Four weeks would not make a big difference."
"The Executive Committee is not a pile of corrupt people. It is just that some people took a wrong turn," said Mayer-Vorfelder, who headed the DFB from 2001 to 2006 and is still active in FIFA circles.
Other FIFA sources have told Reuters they expect the vote to go ahead as planned on December 2 and FIFA have given no indication it intends to change the date.
Last week, two members of FIFA's executive committee were provisionally suspended on suspicion of selling their votes in the contest to host the two tournaments.
Nigerian Amos Adamu and Tahiti's Reynald Temarii were banned from all football-related activity for 30 days while FIFA's own ethics committee investigates allegations they offered to sell their votes when approached by Sunday Times journalists posing as lobbyists for an American consortium.
FIFA is due elect the hosts of the two World Cup tournaments on December 2 in Zurich and may be held by 22 of the 24-man executive with Adamu and Temarii banned from voting.
