The Labour parliamentary party will meet in Leinster House to decide its approach to any further talks on government formation.
Earlier this week, party leader Ivana Bacik held discussions with both the leaders of Fianna Fáil and Fine Gael.
She will update her party on the outcome of those talks.
Speaking to reporters at Leinster House, Ms Bacik said she is seeking a meeting with Fianna Fáil leader Micheál Martin and Fine Gael leader Simon Harris early next week to give them a chance to provide "a substantive response" to Labour's policy priorities.
Ms Bacik said that due to the "reasons outlined" it is "unlikely" Labour will ultimately enter government, she wants the larger parties "a chance to let us know if there's any basis for commencing negotiations".
She separately said she has launched an investigation into how a note from an internal Labour meeting was leaked to the Irish Independent earlier this week, suggesting the party is only speaking to Fianna Fáil and Fine Gael out of courtesy.
Ms Bacik said the note "was not accurate" as it did not take account of the full context of the meeting, and that she was seeking an internal investigation and potential disciplinary action.
Asked what that action would involve, Ms Bacik said "clearly expulsion from the party", before clarifying that she meant the disciplinary measures could mean expulsion and that no pre-defined decisions would be made.
Both Mr Martin and Mr Harris have said good progress is being made in discussions between their parties on forming a government with the focus on agreeing a policy agenda for the incoming Dáil.
Mr Harris was asked whether there was any more clarity on how a rotating taoiseach position might work and the duration of the respective terms in office.
"That doesn't preoccupy much of my time at all," he said.
"I believe there will be a rotating taoiseach and I think that's important.
"It's not important in relation to individuals, it's important in reflecting the mandates that the parties received during the General Election."
Mr Martin said it still was not clear to him whether either the Social Democrats or Labour had the appetite to enter government, but he expected clarity on that in the coming days.
"If we take the Independent route, we do need to make sure that the government lasts five years and that is my agenda, to make sure that it goes full term.
"That means the sufficiency of support behind the government that would enable it to go full term, and that's a factor in that consideration," Mr Martin said.
Meanwhile, the Sinn Féin parliamentary party held a detailed discussion on government formation talks earlier.
Party leader Mary Lou McDonald reported back on her engagement with other parties.
The meeting heard that the numbers allow for Fianna Fáil and Fine Gael to form a government with the support of Independents.
Sinn Féin also nominated TD Aengus Ó Snodaigh to be the next Ceann Comhairle of the Dáil.
In a statement, Ms McDonald said Mr Ó Snodaigh has "a sharp intellect" and, if elected as Ceann Comhairle will "carry out the duties fairly in the public interest".
Mr Ó Snodaigh's nomination follows confirmation by the Regional Independents this week that they will nominate Independent Wexford TD Verona Murphy as Ceann Comhairle.
The Ceann Comhairle of the outgoing Dáil, Fianna Fáil TD Seán Ó Fearghail, has also expressed an interest in remaining in the role, as have his party colleagues John McGuinness and Michael Moynihan.
The vote on who will be the new Ceann Comhairle will take place when the Dáil returns on Wednesday.
