Acting Taoiseach Enda Kenny of Fine Gael and Micheál Martin of  Fianna Fáil hope to avoid a second election.
Mr Martin has said his party will facilitate a minority government, but will not support a programme for government.
Water charges are one of the main sticking points to reaching agreement.
A commission to consider the future of national water utility Irish Water is one of the proposals being considered.
Fianna Fáil want to see the immediate removal of water charges, but Fine Gael see a role for them.
Following the election, almost two months ago, Fine Gael had 50 seats, Fianna Fáil 44, Sinn Féin 23 and the Labour Party got seven.
But no party was able to form a majority government and TDs have so far failed to elect a taoiseach.

Language was spelled "langauge" in the original release, put out on Thursday.
But it was corrected by officials after Twitter users ridiculed the error.
BBC Radio 4 presenter Anita Anand said it was "beyond parody" that the Home Office could not spell language in a note to migrants who have been told to learn English.
A Home Office spokesman said: "This was a regrettable typographical error that has now been corrected."
On Monday, Prime Minister David Cameron announced a Â£20m fund to teach Muslim women in the UK to speak English, claiming it would help tackle segregation and help them resist the lure of extremism.
But some Muslims have accused him of wrongly conflating the two issues.
Mr Cameron said all those who entered the UK on the five-year spousal settlement programme - not just Muslim women - would have to sit language tests after two and a half years.
Thursday's press release said the new requirement would not be implemented before October 2016, with the precise timing and further details to be confirmed by the Home Office "in the next few weeks".
Negotiators from Ireland's two biggest parties are to meet for a final effort to form a minority government.
[NEXT_CONCEPT]
Red-faced officials at the Home Office have been forced to correct a spelling error in a press release about new English language tests for migrants.