Fine Gael has made "no secret" that they want a third party to join government, during meetings with Independent TDs.
Negotiating teams from Fine Gael and Fianna Fáil met with independent Sligo–Leitrim TD Marian Harkin and Roscommon–Galway TD Michael Fitzmaurice on Monday for around 90 minutes.
During the constructive meeting, Tanaiste Simon Coveney reportedly told the TDs that Taoiseach Leo Varadkar specifically has stated his preference for a third party, as well as independents, to form part of a coalition government, in the name of stability.
"It would be clear that they, Fine Gael want a third party involved, they said the Taoiseach had said that he wants another party, and they're meeting the other party leaders in the coming days, and we're going to meet again," Mr Fitzmaurice said.
"Personally, I think the independents are well fit to form this coalition alone, so I don't think it's needed.
"We have given them a document with our policies which we would like to see implemented, which was formed both before after the pandemic started.
"They will send us questions in a few days on the document, and we will send our own list of queries back to them.
"First of all we need to know what the current spend will be, how we're going to kick start the economy, and give it the injection and finance required.
"We've also given them a comprehensive document on rural issues and agriculture that we would like to see implemented."
Likewise, Marian Harkin says that smaller parties like the Greens, Social Democrats and Labour should make up their minds about government formation.
"My view is, we are negotiating the table as an independent grouping we're not looking over our shoulder to see who else is there, to see who might provide cover.
"People say; 'Independents can be picked off, and the truth is they can, but you shouldn't go into politics if you're worried about that, if you are, stay home.
"If you go into politics, you take the good and not so good, and if fundamental policies can't be delivered, what's the point?
"We have no prerequisites, we have no red lines.
"If one party comes along and says yes, that changes it a little, or vice versa and says no, we have the pieces, it will be how to put the jigsaw in place."
Ms Harkin adds that it's not just about rural issues for her and Michael Fitzmaurice but that they would be asking the larger parties to prioritise developing a balance regionally.
"I made it clear I wasn't asking for a bigger cake, but a fair share of it.
"It looks like the cake is smaller now, but what we need is balanced regional development, that has to be stitched into policy."