People Before Profit TD Richard Boyd Barrett says it is 'logical' that his party will support Sinn Féin's Mary Lou McDonald in her bid to become Taoiseach.
Representatives from Solidarity - People Before Profit are due to meet with Sinn Féin today as government formation talks intensify.
It comes ahead of the first sitting of the 33rd Dáil tomorrow, where TDs will be asked to vote on who will become the next Taoiseach.
The leaders of the largest parties - Fianna Fáil, Sinn Féin and Fine Gael - are all expected to be among those nominated, although as of now no candidate yet commands a majority of support in the Dáil.
Leo Varadkar and his ministers will continue in a caretaker capacity until a new government is officially in place.
Deputy Boyd Barrett said his party will be supporting Sinn Féin leader Mary Lou McDonald in the hopes of forming a left-government.
He told The Pat Kenny Show: "[Sinn Féin] won the biggest vote of any party, and they're the biggest component of forces that put forward a left-type manifestos in the election.
"Logically, Mary Lou McDonald is the one who would be capable of assembling a left government that would include or get the support from Greens, Social Democrats, left independents, People Before Profit, Solidarity..."
He also noted that either Fine Gael or Fianna Fáil abstaining from the Taoiseach vote could be enough to get Deputy McDonald elected as the next head of government.
Deputy Boyd Barrett also said his party will not be putting one of their own members forward as a potential Taoiseach, despite having done so last time.
He suggested Taoiseach Leo Varadkar is 'speaking out of both sides of his mouth' by saying Fine Gael is preparing to enter opposition while also standing to be Taoiseach.
The Dun Laoghaire TD said: "This time, we think there is a real and tangible possibility that a left government could be created.
"We think there is an overwhelming desire expressed by the electorate to break the cycle of Fianna Fáil and Fine Gael."
Meanwhile, Fianna Fáil's Thomas Byrne said Micheál Martin will 'absolutely' be standing for Taoiseach tomorrow.
Deputy Byrne said: "We're the party with the largest number of Dáil seats, so I think there absolutely is an entitlement to propose Micheál Martin as Taoiseach.
"I know he's not going to be successful tomorrow, but I also know that after tomorrow I fully expect that full-scale talks will take place between various parties."
He also said there would be no use in putting forward a government that will "limp along" and could be quickly taken down.
Mattie McGrath of the Rural Independent group says their six TDs will meet today to discuss who they will vote for tomorrow - although noted there is no group whip, so the individual deputies can each make their own decision on who to vote for.
He said the group is 'entering talks' with Sinn Féin, but added that he hasn't personally been canvassed by any of the candidates to be Taoiseach so far.