Independent TDs have been offered special deals to become part of the next government.
Sources said the arrangements would be similar to the ones between Fianna Fáil and the late Jackie Healy Rae in the past.
They would include constituency promises and preferential access to ministers.
The leaders of Fine Gael, Fianna Fáil and The Green Party met with Independents Michael McNamara, Marian Harkin and Michael Fitzmaurice on Wednesday.
They will hold further meetings with the Regional Independents group on Thursday.
Meanwhile Tánaiste Simon Coveney has said he will not support the Occupied Territories Bill in any programme for government.
It has become one of the sticking points of government formation talks.
Fianna Fáil and The Greens support the bill, which would ban Israeli products made in the Occupied Palestinian Territories.
TD Gino Kenny appealed to Mr Coveney to support the bill in the Dáil.
But Mr Coveney replied: "No I won't - I don't believe we can do that.
"I've explained it to Senator Frances Black, who brought it forward, and I've huge time for Senator Black - and I understand what she wants to achieve with this legislation.
"But I don't believe that we can do what she's asking for this bill to do legally".
Reporting by: Sean Defoe
