The Fianna Fáil leader Michéal Martin says he would be willing to go into a coalition with Fine Gael.
It follows policy discussions with Leo Varadkar's party yesterday.
The two parties have not yet started any formal negotiations, and Fine Gael has repeatedly insisted it is still preparing to go into opposition.
However, Deputy Martin this morning said he would be willing to go into coalition if a programme for government can be agreed.
He told RTÉ that he believes the next government must move beyond a confidence & supply style arrangement, and that nothing has been ruled in or out when it comes to the prospect of a rotating Taoiseach.
Both parliamentary parties met earlier today to be briefed on the talks between the two parties yesterday.
This afternoon Fine Gael officials said the party is still expecting to be in opposition when the next government is formed.
Fine Gael says parliamentary party updated on talks with Fianna Fáil and the Greens. Says good exploratory discussions but seemingly no change in position
— Seán Defoe (@SeanDefoe) March 5, 2020
TD Neale Richmond said the party hasn’t ruled out a coalition, but there is more talking to be done:
“We said before the General Election that we would be prepared to go in for a coalition, that wasn’t an issue,” he said.
“The thing is that on foot of the election results that we received we need to see how we can advance our programme.
“There are other parties that are bigger than us; there are other groupings that have spent the last four or nine years trying to get us out of government.
“So, we have to be quite clear that any discussions any conversations about policy we have, we still have an agenda we want to put forward and that hasn’t changed just because of the election results.”
Fine Gael Finance Minister Paschal Donohoe reiterated after yesterday's meeting that his party doesn't need to be involved in the next government.
He suggested there are "many governments possible" within the current Dáil.
The Dáil is meeting for the second time this afternoon, but there will be no votes for Taoiseach.
So little progress has been made over the past two weeks that most TDs feel it would be a waste of time to have votes that won't lead to any result.
Instead, the chamber will debate the coronavirus and hear statements on the recent European Council meeting and Brexit negotiations.
Both the Fine Gael and Fianna Fáil parliamentary parties meet today ahead of the second sitting of this Dáil.