The Taoiseach Leo Varadkar says he is hopeful a new government can be in place by June.
Both Fine Gael and Fianna Fáil have agreed to enter government together - but need a third party to make up numbers in the Dáil.
The Green Party has been discussing the prospect in recent days.
However it is understood its TDs are split on the move.
While members of the Green Party are meeting this weekend to discuss it.
During the week the party set out its demands - however a key target of reducing carbon emissions by 7% was not agreed in a response.
On Friday Mr Varadkar said it was something he would like to work towards.
But Newstalk's political correspondent, Sean Defoe, believes the Greens are still a way off entering formal discussions with the other parties.
"They've had three meetings since the Fianna Fáil and Fine Gael reply to their requests came earlier on in the week.
"Those are going to continue over the weekend.
"But at the moment it looks a very, very long way from the two-third majority of Greens you would need to approve any sort of deal - let alone even start the talks".
"[The Green Party] effectively have two different camps: one that is saying we have 10 years to save the planet, we have been given the biggest mandate we've ever been given - it's going to be difficult to get everything done in economically uncertain times and with these two parties - but the best thing to do is go in and try to do it.
"And the other side are arguing that really Fine Gael and Fianna Fáil aren't very serious about these climate targets, it's going to be what happened in 2007 - we'll be destroyed electorally and nothing is going to get done for the climate".
Reporting by Sean Defoe
