Taoiseach Leo Varadkar has offered Independent TDs a deal similar to that given to former Kerry Independent Jackie Healy-Rae to support a coalition between Fianna Fáil, Fine Gael and the Green Party.
Mr Varadkar made the offer at a meeting in Government Buildings with a number of Independents, as well as Fianna Fáil leader Micheál Martin and Green Party leader Eamon Ryan on Wednesday.
The meeting was attended by TDs Marian Harkin, Michael Fitzmaurice and Michael McNamara. Advisers for Mr Martin, Mr Varadkar and Mr Ryan were also present.
Sources said Mr Varadkar offered a deal for Independents similar to that struck with the late Jackie Healy-Rae by Fianna Fáil governments in the past. Mr Varadkar specifically cited the late Mr Healy-Rae, as well as former Independent Mildred Fox.
Such an arrangement, Mr Varadkar is understood to have said, would involve deals for individual TDs as well as access to government ministers.
The Independents were told they will be given a Programme for Government when it is agreed, and were left with the impression that they would be supporting an administration from outside. It is understood that no ministerial posts or committee chairs were offered.
Sources said Mr Varadkar referenced a number of arrangements Independent TDs had with previous governments.
There are further meetings with the Regional Independents group and Mr Varadkar, Mr Martin and Mr Ryan tomorrow, Thursday.
Talks will also continue between the three main parties with a deal expected to be concluded next week.