Taoiseach Enda Kenny has said the payment made by FIFA to the FAI is "quite extraordinary", and questions should be answered by FAI CEO John Delaney.
Speaking at a press conference after today's North-South Ministerial Council meeting, Mr Kenny said Mr Delaney's position is tenable.
Mr Kenny said he is "quite sure" Mr Delaney will answer any questions that need to be answered.
The Taoiseach added the FAI will make a statement shortly in the interest of accountability and transparency.
Earlier, former FAI chief executive Fran Rooney said the revelation of a €5m payment from FIFA puts the FAI in a bad light.
Speaking on RTÉ's Morning Ireland, Mr Rooney said it is almost "nonsensical to think that we had a case to take legal action.
"All decisions in football are final, and it didn't stop us going to the World Cup. It stopped us from getting a penalty shoot-out."
He said he does not know where FIFA was coming from agreeing to a settlement.
Mr Rooney added that the big issue for FIFA particularly after last week's events is transparency in all aspects of the game.
"Confidential payments are at odds with transparency.
"This [payment] should have been disclosed at the time. It should have been disclosed by FIFA and the FAI."
Mr Rooney called on the FAI to publish the legal agreement of the payment and let the public see what is in it.
He said that on the international arena, the payment will be seen as a very bad reflection on FIFA and the FAI and he called for a probe into the whole arrangement.
"In some ways it was a good deal, but it's not about the deal, it is about how it is presented and disclosed to the public and the international arena."
He also said that the payment "doesn't seem to have been reflected in FAI accounts for a number of years. It is not clear where that money was showing in the accounts and I am calling on the FAI to show where that money is clearly in the accounts."
Tánaiste Joan Burton has described the awarding of €5m to the FAI by FIFA as "a very intriguing story, particularly the meeting where you walk in, have a few hot words and leave with five million."
Minister for Sport Paschal Donohoe has said questions surrounding the €5m are primarily a matter between the FAI and FIFA.
However, he added they are also a public matter and questions on the money and transactions need to be answered by the FAI.
Mr Donohoe said there are no issues arising over Government funding to the FAI.
On RTÉ’s Today with Sean O’Rourke, solicitor Damien Tansey said: "In my view there isn’t a lawyer in the common law world who would suggest that there is a good cause of action available to the FAI against FIFA arising from the Thierry Henry handball".
He cited a principle in law - 'volenti non fit injuria' - to the willing there is no redress.
Mr Tansey said the FAI did not have a case against FIFA following the handball incident as when players take to the field they are essentially agreeing to leave the decision of the referee on the field.
Meanwhile, former Republic of Ireland international player and assistant manager Liam Brady has said neither the staff nor the players knew about the €5m payment.
Also speaking on Morning Ireland, Mr Brady said it was "mind-boggling".
He said he knew FIFA was under pressure to compensate the FAI, but he did not realise the FAI got as much money as it did.
Mr Brady agreed that if sporting bodies were to pay money for refereeing errors it would lead to a "nightmare scenario".
Sinn Féin's spokesperson on Sports, Dessie Ellis, has called for the Oireachtas Committee on Sports to request the attendance of FAI Chief Executive John Delaney in order to further explain a €5m payment.
Mr Ellis said: "It is in the best interests of the FAI and football as a whole that the Oireachtas Committee and Mr Delaney can meet for a frank discussion on this payment rather than allow rumours and doubt to grow over the actions of our national football association on the international stage."
