Fine Gael leader Simon Harris has confirmed that he will be talking to the Independent TDs, who he said, have in the past supported the Government, to see if they are minded to do so again.
Speaking at Fairyhouse Racecourse in Co Meath, Mr Harris said it was a natural part of the process in the run up to the election of taoiseach in a Dáil vote on 9 April.
Deputies Denis Naughten, Peter Fitzpatrick, Noel Grealish, Matt Shanahan and Cathal Berry confirmed that they expect to meet Mr Harris.
Another independent TD considered to be weighing up his options is Michael Lowry.
The coalition has a slender majority and does not need the support of Independents, however the Government would welcome being able to count on some support.
Confirming he would meet the Fine Gael leader, Mr Grealish said: "Yes. I will be meeting him before the vote on 9 Tuesday."
Likewise, Mr Naughten said in a text: "Yes. Will be meeting him."
Mr Fitzpatrick said he had spoken to Mr Harris on the phone and would be meeting him before the return of the Dáil.
Deputy Shanahan said: "I'm looking forward to hearing him reiterate his significant concern to address the many stalled investments in Waterford, a number of which he was/is directly involved: cardiac schedule and promised capital builds at University Hospital Waterford, as well as comprehensive funding to South East Technical University and airport."
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Independent TD Marc McSharry has already indicated that he will back Mr Harris in the vote next week due to his "personal attention to the amalgamation of St Angela's College with the Atlantic Technological University".
Twelve Independent TDs have already indicated they will vote against Mr Harris.
They include: Verona Murphy, Michael Healy-Rae, Danny Healy-Rae, Violet Anne-Wynne, Marian Harkin, Mattie McGrath, Michael McNamara, Thomas Pringle, Michael Collins, Michael Fitzmaurice, Richard O'Donoghue and Joan Collins.
Sinn Féin's Matt Carthy called on Independent TDs last week to vote against Mr Harris and trigger a general election, declaring that supporting the new Taoiseach means Independents will be "... voting for a continued crisis in housing, health and disability services, and in the cost-of-living".
Regarding any changes in his Cabinet, Mr Harris said that "these were issues that he will think about in the days ahead".
"For me," he said, "the priority right now is on policy and delivering.
"We have the Fine Gael Ard Fheis in Galway at the weekend, which will provide a further opportunity to outline to the Irish people some of the areas where he wants to make real progress."
Separately, the Fine Gael leader said that he was very concerned about the trend in road deaths, and that his office has reached out to the Road Safety Authority.
Mr Harris said that he would hope to have one of his very early meetings in government with the RSA, the gardaí and others.
He praised An Garda Síochána for its road safety campaign over Easter. He also described the number of arrests for drink driving so far this Easter weekend as "alarming".
