Enda Kenny could offer a five year deal to Independents and smaller parties, in an attempt to form a rainbow government.
It is reported that it will be a five year deal that would remain in effect even if Mr Kenny himself was not Fine Gael leader or Taoiseach.
The Irish Times reports that Fine Gael have been negotiating with members of the Independent Alliance, the Green Party and several other Independents.
Any deal to form a minority government would still need an agreement of some kind with Fianna Fáil.
Meanwhile a business specialist has said pressure from people will force political parties to act to form a government.
David Kelly from IndEx Partners deals regularly with interim managers in companies.
The outgoing government are continuing in their roles until a new one can be formed, with some speculation that it could cause instability.
Mr Kelly has said that sooner or later people pressure will force parties to act.