Green TDs are divided over whether the party should enter government with Fianna Fáil and Fine Gael.
Party sources say leader Eamon Ryan is in favour of the Greens ultimately doing a deal with the two parties if efforts to form a national unity government fail.
Carlow-Kilkenny TD Malcolm Noonan said if a unity government cannot be formed then "the only realistic scenario for a stable government is Fianna Fáil and Fine Gael and I am more than willing to talk to them".
However, a number of new TDs yesterday denied the Greens were open to talks with the parties after a senior party source told the Irish Independent that a coalition with Fine Gael and Fianna Fáil cannot be ruled out if a unity government is not possible.
Finance spokesperson Neasa Hourigan said that the Greens want to be in government "but the Covid crisis is not the time for programme for government talks".
"We're focusing all of our energies on putting forward a reasonable and palatable proposal for unity government," she said.
Her view was supported by TDs Roderic O'Gorman and Patrick Costello, who said jointly: "We're asking people to pull together as a country, why aren't politicians doing the same thing?"
Mr Ryan is said to be among those who are enthusiastic to return to Government but he is facing resistance from newer members of the parliamentary party, according to three separate Green Party sources. Mr Ryan did not respond to a request for comment.
Mr Noonan denied there was a split, but acknowledged there was a "difference of opinion and it may be significant".
He said anything negotiated would ultimately have to be voted on by members. "Fine Gael and Fianna Fáil is the only option for a stable government. It's bound to be the case there are differences of opinion about the strategy," he said.
It comes as Fianna Fáil and Fine Gael began talks on a programme for government yesterday which are expected to last around a fortnight.
The two parties issued a joint statement after what was described as a "productive" meeting. "They both agree the need to form a strong, stable government that will help Ireland recover post-Covid-19. They are working to develop a programme for government that provides stability and majority support in the Dáil," the statement said.
Meanwhile, Ceann Comhairle Seán Ó Fearghaíl has warned politicians will be unable to pass any new laws after this Sunday, creating a "very serious Constitutional problem".
In an email to Fianna Fáil TD Marc MacSharry, Mr Ó Fearghaíl confirmed, based on legal advice, that it is not possible for the new Seanad, which will be elected next week, to meet until 11 people are nominated to the upper house by a Taoiseach elected by the current Dáil.
"This obviously gives rise to a very serious Constitutional problem: from midnight next Sunday, March 29, 2020, the Houses of the Oireachtas will not be able to pass legislation."
However, senator and former attorney general Michael McDowell said the question of whether or not the Seanad could sit in the absence of the 11 Taoiseach's appointees was considered in 2016 and that legal advice then was that it was capable of meeting and continuing to operate.
Taoiseach Leo Varadkar put pressure on the Greens, Independents and small parties to enter government talks.
He said that a new government would need to last for the next four years and have "a stable working majority" that would require at least 10 more TDs in addition to those from Fianna Fáil and Fine Gael.