Fianna Fáil leader Micheál Martin has said he is "hopeful" that a new government will be formed by 22 January, adding that it would be "nice to be up and running" as the new United States president takes office.
Mr Martin also said there has been fairly significant progress made on policy in the government formation talks that have taken place over the last couple of days.
He said discussions were ongoing regarding the structure of the government and nothing had been finally agreed in terms of the rotating Taoiseach.
Mr Martin would not be drawn on reports that he will serve for three years, with Fine Gael leader Simon Harris due to serve for two years.
He said he would not pre-empt anything, adding that there had to be a Dáil vote and agreement with Fine Gael and Independents.
He described discussions with Independent Kerry TDs Michael and Danny Healy-Rae as "substantive" and said it was about ensuring a government that would sustain five years.
Talks between Fianna Fáil, Fine Gael and Independent Ireland are expected to get under way tomorrow.
Invitations have now been issued to the party, which has four TDs; Michael Collins, Richard O'Donoghue, Michael Fitzmaurice and Kenneth O'Flynn.
Discussions with the Regional Group of Independent TDs and Michael and Danny Healy-Rae are set to take place before the end of the week, but no time has been confirmed yet.
The Regional Group of Independents will be represented at the talks by Michael Lowry, Marian Harkin and Seán Canney.
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Mr Harris also said the parties were working to have a new government in place by 22 January, but he added that this was a tight deadline.
Some of those involved in the talks believe the task of having everything in place by that date is too great and it could take a little longer.
After the Social Democrats exited the government formation process yesterday, the focus will now turn to seven regional independent TDs along with Michael and Danny Healy-Rae.
Speaking on RTÉ's Morning Ireland earlier, Michael Collins, the leader of Independent Ireland, said his party is available for talks "based on the policies of Independent Ireland, not on parish politics".
He said that Fine Gael and Fianna Fáil seem to want to talk to the Regional independent Group, "which they are well entitled to do", but that these talks would likely be "based on parish politics".
"It's not going to be based on policies that deliver on housing, deliver on farming, deliver on fishing, deliver on health, deliver on a cost of living and transport," he said.
"These are the areas that our policies focused on."
Mr Collins said his party is calling for a minister for fisheries, marine and the islands "because it's an industry that has been forgotten for the last five years".
Additional reporting by Mícheál Lehane
