Fine Gael TD Noel Rock says the FAI has major questions to answer in relation to its corporate governance structure.
He says he made a complaint to the Office of the Director of Corporate Enforcement.
Today it was revealed the organisation had been paying €3,000 a month to rent properties for the use of former chief executive John Delaney.
He stepped aside into a more junior executive role last night.
"This accommodation is worth €3,000 per month, €36,000 per year, in an organisation where the chief executive has to loan €100,000 to the organisation itself," Deputy Rock said. "There is a lot going on at the FAI."
"There are major questions to answer over the bridging loan provided by the Chief Executive of the FAI to the organisation," said Fianna Fáil spokesperson on Transport, Tourism, and Sport Robert Troy.
“The larger question remains. The uncertainty around the loan must be answered and I expect John Delaney to come before the Oireachtas Committee in early April or sooner to answer this, explain the remit of the new role, and if his actions were not becoming of a CEO why should he take up an executive vice president role within the FAI.
“The FAI has indicated their willingness to bring forward their appearance before the Oireachtas Committee and I will be raising this possibility at our Committee sitting this week,” Deputy Troy added.
Earlier today, the FAI announced that Delaney's new role would mean he would take a pay cut.
A statement issued by the association said: "As regards John Delaney's salary in his new role as Executive Vice-President, the FAI can confirm that the salary is substantially less than the salary he previously received as CEO."