John Coates said FIFA must make the bidding system more transparent and respond to the damaging scandal, detonated by England's former FA boss earlier this week.
"Mud does stick... so it is damaging," the Australian Olympic Committee president told the AAP news agency. "It's not good for FIFA's image. I really hope they will address things.
"Even if there's no evidence, at least there's a perception out there that there's something wrong."
Former English Football Association chairman David Triesman earlier this week accused four FIFA executive committee members of asking for favours in return for World Cup votes.
Members of British Parliament involved in an inquiry over England's failed 2018 bid said the Sunday Times newspaper had evidence that two other FIFA executive committee were allegedly paid $1.5 million to vote for Qatar's successful bid for the 2022 World Cup.
Triesman gave evidence on Tuesday to the inquiry into why England failed to secure the 2018 finals, which went to Russia, at the vote in Zurich, Switzerland last December.
Australian received only one vote in the 2022 race while England got just two.
"It is important that all bidding systems, whether for Olympic games, World Cups or world championships... are above board and conducted with full integrity," Coates said.
"The onus is now back on FIFA to investigate its own."
Coates insisted FIFA needed to follow the lead of the International Olympic Committee (IOC), which took action after its own corruption scandal in the bid race to host the 2002 Winter Olympics in Salt Lake City.
"We're in the last month or so of where the 2018 Winter Olympics goes and they're spending something like $70 million on their bids, these cities," he said.
"There's been no suggestion of any impropriety there but there was previously and 14 IOC members were shown the door after Salt Lake City.
"One of the lessons FIFA's probably learning is that it's certainly open to abuse," added Coates, who also said Australia could struggle to fund future World Cup bids unless changes were made.
"Whether there's money changing hands or not, but in trading votes when you put the decisions on two World Cups together."
