The Labour party is considering forming another coalition with Fine Gael as part of a minority government.
A party spokesperson has confirmed this is one of three options being considered.
The other options for Labour include supporting a Fine Gael-led minority government from the opposition benches or taking an "outright opposition position".
However, it is understood there are very mixed views among the seven Labour TDs about the prospect of going back into government with Fine Gael, with some said to be "keener than others".
Any move to form another coalition could only happen after Fine Gael and Fianna Fáil had agreed how a minority Government would work, the Labour spokesperson said.
Outgoing Labour Minister Alex White confirmed that an approach had been made by the Taoiseach and Fine Gael for the Labour Party to join them and others in government.
But he said this was at a "very, very early stage" and that it would be quite premature for anyone to assume that the party has made any decisions or looked at that propositions in any detail
Contact between Fianna Fáil and Fine Gael will continue over the weekend with formal talks set to resume on Monday.
Talks between Labour and Fine Gael are ongoing given that the parties meet regularly as partners in the caretaker government and this is set to continue.
Two "impromptu" meetings took place between the leadership of both parties last week.
Labour said this was a "listening exercise for the party".
Any decision to form another coalition with Fine Gael would have to get the backing of a Labour party delegate conference.
The mood within the party was against returning to government in the aftermath of the election results and the party's TDs are said to be unsure if that sentiment has altered significantly in recent days.
The spokesperson said the party will also hold an election strategy meeting early next week to be prepared in the event of a general election being called suddenly.
Meanwhile, Fine Gael's TD for Meath East, Regina Doherty, said she would love to see Labour, the Green Party and the Social Democrats in government adding that there is no reason they can't work together.
She said a deal between the two parties is very close and that she expected it to be concluded within the next ten days.
Fianna Fáil's Thomas Byrne said his party accepts that Fine Gael need the support of other TDs to allow it to back a minority government but that they cared more about the policies of that government rather then the personalities or the people that it was made up of.
He said the party is currently looking at precedents for minority governments in other European countries to understand how it would work in practice.
