Former FIFA vice-president Jim Boyce has admitted that he is "absolutely astounded" to learn that the governing body paid the Football Association of Ireland a financial settlement to prevent legal action in 2009.
FAI chief John Delaney revealed on Thursday that around £3.6m was offered to the organisation for them to not contest in court their infamous World Cup playoff defeat.
Thierry Henry's controversial handball in the build-up to William Gallas's winning goal denied the Republic of Ireland a place in the following year's finals in South Africa.
Boyce now wants an investigation to be launched looking into why the payment was authorised.
"How anyone can authorise a payment of $5m (£3.6m) to stop legal proceedings is totally beyond me," BBC Sport quotes the Irishman as saying.
"If this was authorised by the president of FIFA without the knowledge of the executive committee - this is something that has to be looked into.
"I'm absolutely astounded. I have never heard anything as ridiculous in my life. If a payment of €5m has been paid because of a handball and threatened legal action, then I hope a full investigation will be carried out into this and any other such arbitrary payments."
In response, scandal-hit FIFA last night claimed that the payment was intended as a "loan" to be repaid in full if the Green Army qualified for the 2014 World Cup, which they failed to do.