If an outgoing leader cannot form a government their name goes before the parliamentary party
Returning Fine Gael TD Richard Bruton cannot say if Enda Kenny will lead the party into the next election.
He also says they have not ruled out going back into government with Labour as a partner.
"The Labour Party continue to be a very important part of this Dáil, so we will be talking to all parties", he told Newstalk Lunchtime
But Mr Bruton also clarified that Taoiseach Enda Kenny "clearly won't be talking to either Sinn Féin or the Anti-Austerity Alliance".
On the prospect of talking to Fianna Fáil, he replied: "The party is continuing to reflect on the result".
"While the party recognises that we lost the election, I don't think the party is going...around feeling that we have lost everything", Mr Bruton added.
The final picture of the 32nd Dáil has Fine Gael on 50 seats, Fianna Fáil on 44, Sinn Féin 23, Labour 7, Anti-Austerity Alliance-People Before Profit 6, Social Democrats 3, Green Party 2 and Independents on 23.
On the election result, Mr Bruton said: "There was no sense of blame - we learn from the mistakes (we) made".
"There was an open recognition that mistakes were made by lots of us, by everyone".
Fine Gael and Fianna Fáil held their first parliamentary party meetings since the election on Thursday, as negotiations and talks are continuing.
But Mr Bruton could not say if Mr Kenny would lead the party into the next general election.