Fine Gael need six more TDs for a minority administration
Senior figures in Fine Gael have said that they expect a new Government to be in place by Thursday of this week.
Defence and Agriculture Minister Simon Coveney is hopeful his party will be able to strike a deal with Independent TDs to see Enda Kenny elected Taoiseach in the coming days.
Fine Gael need six more TDs to support them before they can set up a minority-led administration.
The Defence Minister has also appealed to the Greens and Social Democrats to be supportive of a new Fine Gael Government.
John Downing is a political correspondent with the Irish Independent, and he says the Government could become reliant on facilitation from the SocDems and Greens.
"There are three Social Democrat TDs and there are two Green Party TDs - both have said they do not want to participate in Government.
"The Greens have said they would consider supporting the Government from the Opposition benches."