Formal negotiations on a programme for government will begin this Thursday.
It follows a meeting of the leaders of Fine Gael, Fianna Fáil and the Green Party.
Leo Varadkar, Micheál Martin and Eamon Ryan sat down on Tuesday to lay out a timeline and ground rules for the talks.
Mr Ryan has said he hopes programme for government negotiations can finish by the end of the month.
"My preference would be kind of thinking about 'well we should try and get this done by the end of the month'.
"It'll take a little bit of time then to go to - we'll probably have to do a postal ballot like other parties, and that'll take a period of time.
"But I think the Irish public would [expect] this to be done in a matter of weeks rather than longer, and I'd share that".
It comes after the Greens agreed over the weekend to enter government formation negotiations with the two largest parties.
The Greens have insisted a 7% carbon emissions reduction target is a red line for the party in the negotiations.
It is far from guaranteed that they will ultimately enter government, with several TDs warning if they do not like what is on the table they will walk away.
Even if a programme for government is agreed, it will need to be approved by two-thirds of the Green Party membership - with many in the party opposed to a deal with Fine Gael and Fianna Fáil.
Meanwhile, a Fianna Fáil TD has acknowledged there is some unease within the party about the prospect of a coalition with Fine Gael or the Greens.
Niall Collins told The Pat Kenny Show he believes there's a "silent majority" of party members who recognise the need to form a government as soon as possible.
He said: "For this process to develop into a government and evolve into a programme for government, we need to have clarity - and both the membership and the public need to know and understand where this is going.
"I'm just keen to ensure the Fianna Fáil input is front and centre in any programme for government."
