FAI chief executive John Delaney said he is concerned outgoing Fifa president Sepp Blatter may have "done a deal to get his own man in" as his replacement, following his shock resignation.
The FAI boss welcomed the decision by the 79-year-old to step down in the wake of a string of scandals at world football's governing body, but said he would be watching closely to see who emerges as a likely replacement.
He said people should ask "has some deal been done by Blatter with somebody else to come in?"
"Has he done a deal in the last couple of days and said, 'I'm getting out of town, I want my own man in'. That's something I'll be watching carefully, as will many others," he said last night.
He said it was "a good day for world football", adding that he wasn't surprised by the decision, despite Blatter winning re-election just last week.
"There was momentum against him, be it from sponsors, be it the FBI, be it the British government, be it from within football where nearly 40pc of the organisation had the bravery to vote against him," he said on RTÉ news.
He said that world football needed "to move on" and that an overall change within Fifa was needed. He said it was time for a president who "really believes in change".
"We can see the culture of Fifa was one of corruption, one of bribery, nothing to do with the beautiful game, more to do with, as I described it last week, a mafia movie rather than football."
He said Fifa should follow the example set by the International Olympic Committee (IOC), which was previously dogged by similar scandals.
He said the resignation offered "a once-off opportunity" to transform world football.
Asked who he would like to see come into the role, Mr Delaney said Uefa president Michel Platini would "get a lot of support within Uefa and possibly outside".
He said he was proud of the position the FAI had adopted in opposing Blatter's re-election.
"I'm glad we took the position we did and I'm glad we took it early," he said, adding that Ireland didn't "jump on the bandwagon like other nations".