Micheal Martin is edging towards becoming the next Taoiseach with Leo Varadkar prepared to allow the Fianna Fail leader to serve the first term in the office.
The Fine Gael leader is insisting on an equal partnership between him and Mr Martin if they enter into a coalition government.
Mr Varadkar will allow Mr Martin the first term in the office if the two parties agree to rotate the office of the Taoiseach.
However, the caretaker Taoiseach is eager to remain in office during the current phase of the virus emergency.
Agreement on the rotation of the Taoiseach's office over the next four or five years is central to government formation talks between the two parties.
"An equal partnership between Fianna Fail and Fine Gael is a red line," a senior Fine Gael source said.
"Who gets the first spin in office is not," a source said.
Yesterday, Mr Varadkar confirmed the continuation of his tenure in the Taoiseach's office was part of the negotiations.
Asked if he believed he will be Taoiseach next month, he said: "That is something that is up for discussion with Fianna Fail but they are a party who have slightly more seats than us and we recognise that.
"But I don't think anyone's focus is on what jobs they are going to hold in a week's time or few a months' time."
Last night, a senior Fianna Fail figure said Mr Varadkar's comments on Dail seats suggested that he accepted Mr Martin should serve as Taoiseach first.
"He more or less said it would be a Fianna Fail Taoiseach as they have more seats," the source said.
Another front-bench Fianna Fail TD insisted the general election votes meant Mr Martin should serve as Taoiseach first.
"Fine Gael seems to have forgotten the outcome of the general election due to this growing consensus that he should remain as Taoiseach," the source said.
In Fine Gael, there are concerns Mr Martin will not sign up to a 50-50 deal with Mr Varadkar which would see them both serve equal time as Taoiseach.
Fine Gael will not enter into a government arrangement with Fianna Fail if it does not rotate the Taoiseach's office for an equal number of years.
They are also insisting on holding the same number of cabinet positions.
Yesterday, the parties held programme for government negotiations aimed at producing a document which could be presented to others interested in joining their coalition.
After the talks, both Fianna Fail and Fine Gael said they had a "positive meeting and discussion on policy issues".
They both agreed to "keep the dialogue confidential" and said they will contact each other over the coming days.
Speaking at a coronavirus briefing in the Citywest Hotel, Mr Varadkar said he hoped the "joint document" the parties agree will be completed by either this week or next.
"That would allow us to approach third parties like the Greens, Social Democrats and Labour to see if they are willing to form a government because we believe what is required is a government that will last four to five years."
Meanwhile, the Green Party held another meeting yesterday and decided for the third time not to enter into government with Fianna Fail or Fine Gael.