The Green Party is open to a coalition with Fianna Fáil and Fine Gael if it cannot advance its proposal for a national unity government.
Fine Gael and Fianna Fáil have so far rejected the Greens' call for the establishment of an administration involving all parties in the Dáil to deal with the Covid-19 crisis.
While continuing to actively pursue the unity government proposal, a senior Green Party source said a coalition with Fine Gael and Fianna Fáil cannot be ruled out, and downplayed suggestions it would not be supported by the majority of Green members.
It comes as Fine Gael and Fianna Fáil are expected to escalate talks to form an unprecedented coalition government in the coming days.
Fianna Fáil leader Micheál Martin said last night that a government "with a solid majority" has to be formed to deal with the economic fallout from the public health crisis in the second half of the year.
Senior figures in both parties will meet today in a bid to agree on a common policy paper and to move talks onto a programme for government that is now likely to be dominated by measures to deal with the fallout from the crisis.
The Attorney General has advised the outgoing Government it will not be able to pass legislation through the Oireachtas after next week as the new Seanad, which will be elected from next Monday, will not be properly constituted without the 11 nominees of a newly elected Taoiseach.
"Even those of us in the Government have to recognise that the current situation is sustainable for a couple of weeks, but no more," a senior Fine Gael source said last night.
Despite TDs and senators expecting to pass a raft of emergency measures, including income support for laid-off workers and rent freezes, before the weekend, ministers expect that other legislative changes may be needed in the coming weeks as the crisis develops.
Taoiseach Leo Varadkar said the caretaker administration had to be focused on dealing with the Covid-19 health and economic emergency but he said that "to the extent that we can find time, we are finding time" for talks on forming a government.
"We are open to talking to the Greens, Labour, Social Democrats [and] other groups that may wish to speak to us but the priority has to be Covid-19, I think people would expect no less," he said.
Fianna Fáil leader Micheál Martin told RTÉ that in the second half of this year "there will be very significant issues" facing the economy.
He said: "A government that is constitutionally sound and has a solid majority has to be formed to deal with the many, many repercussions - both health and economic - that will flow from this crisis."
In an attempt to sell the national unity government proposal, Greens leader Eamon Ryan has proposed that Mr Varadkar, Health Minister Simon Harris and Tánaiste Simon Coveney remain in their roles to deal with the crisis.
Asked about this idea on Monday, Mr Martin said he had already discussed this with the Taoiseach a number of weeks ago and "we've clear understandings in terms of how that would develop".
Fianna Fáil has declined to clarify what these understandings are.