Sinn Fein's negotiators have told other parties in private talks that they want to form a coalition government with Fianna Fail.
The party has signalled its preference for a "left-led" government with Micheal Martin's party if it cannot form a minor- ity left-wing government without Fine Gael or Fianna Fail, according to TDs who have held discussions with Sinn Fein negotiators.
Sinn Fein's position is likely to put further pressure on Mr Martin, who has continued to rule out any coalition with Mary Lou McDonald.
While he has the support of many in his parliamentary party, a number of Fianna Fail TDs have privately told the Herald in recent days that this position may not be sustainable if a government is not formed.
Sinn Fein's negotiating team, which includes Pearse Doherty, Eoin O Broin, Louise O'Reilly and Matt Carthy, have held talks with the Green Party, Social Democrats, Rise-Solid- arity-People Before Profit and Independent TDs.
Green Party leader Eamon Ryan said Sinn Fein's preference is to include Fianna Fail, the Greens and the SocDems in the next government.
People Before Profit TD Richard Boyd-Barrett said that, while his preference was for a left-wing minority government without either of the civil war parties, Sinn Fein's negotiators had signalled a willingness to govern with Fianna Fail.
"They were keeping open the option of deals with others, which I took to mean Fianna Fail given they are open to talking to them, but they did point out that Fianna Fail don't want to talk to them," he said.
Rise TD Paul Murphy said: "They are saying they are pursuing two options, minority government or what they call left-led government, which is coalition with Fianna Fail.
"We're of course disappointed that they are considering putting Fianna Fail back in power."
Sinn Fein TDs involved in the negotiations did not return calls last night.
The negotiating team have appealed to other parties and Independent TDs that they have met in recent days to back Sinn Fein leader Ms McDonald in the Dail vote for Taoiseach taking place today.
The five Rise-Solidarity-People Before Profit TDs are expected to back Ms McDonald, giving her at least 42 Dail votes, which is likely to be more than either outgoing Taoiseach Leo Varadkar or Mr Martin.
However, she will not be elected Taoiseach as she will not command a Dail majority.
Mr Martin last night appointed a negotiations steering group to meet with other parties, which will report back to its frontbench and parliamentary party.
It includes deputy leader Dara Calleary, children's spokeswoman Anne Rabbitte, finance spokesman Michael McGrath, public expenditure spokesman Barry Cowen, housing spokesman Darragh O'Brien and education spokesman Thomas Byrne.
However, the party's justice spokesman, Jim O'Callaghan, who was involved in talks with Fine Gael on confidence and supply four years ago, is not involved in the delegation.
The Green Party will begin bilateral talks with other parties next week. It is due to meet a delegation from Sinn Fein on Monday, Fianna Fail on Wednesday and Fine Gael towards the end of next week.
The Fianna Fail parliamentary party met last night in Leinster House but did not discuss in detail the ongoing government negotiations.
Mr Varadkar has appointed outgoing government chief whip Sean Kyne to the Seanad for a few weeks in order to bolster Fine Gael's efforts to win seats in the upper house.
Mr Kyne, who lost his Dail seat in Galway West last week, will forego the €5,676-a-month salary to become a senator in the outgoing Seanad until the end of next month.
As a result, he will be able to vote in the forthcoming Seanad elections, which he is also expected to contest, as Fine Gael aims to elect a number of senators, including TDs who lost their Dail seats last week.
The electorate for 43 of the Seanad's 60 seats includes around 1,200 politicians and consists of incoming TDs, outgoing senators and city and county councillors
The appointment of Mr Kyne, who is also Minister of State for the Gaeltacht, arises as a result of the vacancy created by the election of former senator Frank Feighan to the Dail for the Sligo-Leitrim constituency.