Discussions between Fine Gael and the Independents concluded with no agreement on Wednesday.
The two sides ended discussions after 10.30pm with further meetings planned for Thursday.
The five rural TDs, the Independent Alliance, Maureen O’Sullivan and Michael Healy-Rae will be presented with a Programme for Government on Thursday morning.
It is understood the proposed Programme for Government will include new measures to assist those in arrears with their mortgages including the establishment of a new agency.
It is understood there are still some issues to be ironed out including the location of wind turbines, the appointment of judges and concerns surrounding turf cutting.
However, there is optimism that an agreement can be reached on Thursday to facilitate a vote for taoiseach on Friday.
Waterford TD John Halligan met with Minister for Finance Michael Noonan and Minister for Justice Frances Fitzgerald to discuss cardiac care at Waterford Regional Hospital.
It is understood an agreement is close but Mr Halligan is to meet hospital consulates on Thursday morning before accepting the proposal by the two Ministers.
Some of the rural TDs had indicated a desire to bring the proposal to their constituents.
However, Fine Gael sources insisted the latest a vote for taoiseach could be held is Friday.
Acting Taoiseach Enda Kenny had assured Independents he and his party were willing to work through the night to seek an agreement.
Earlier, Mr Kenny said he would like to think “this matter can be concluded by this week” but he could not confirm that.
He was responding to Sinn Féin deputy leader Mary Lou McDonald who asked when the House “could shed some light as to when or whether there will be a vote to appoint a taoiseach and likely to have a vote on the appointment of a taoiseach”.
Mr Kenny said “as the House and the world are aware now an agreement was reached between Fine Gael and Fianna Fáil on a number of important matters”.
He said discussions are taking place with other alliances and groupings who are interested in making arrangements” on the running of the country.
He said the talks were not taking place “in virtual reality”.
“They are very real.”
Some of the rural TDs had indicated a desire to bring the proposal to their constituents.
However Fine Gael sources insisted the latest a vote for Taoiseach could be held is Friday.
Mr Kenny had assured Independents he and his party were willing to work through the night to seek an agreement.
