Leo Varadkar and Micheál Martin are expected to meet on Tuesday for exploratory talks following the Irish general election.
It will be the first sit down discussions between the Fine Gael and Fianna Fáil leaders since the election.
On Monday, Mr Varadkar said the talks did not signal a change in his party’s approach to government formation but were “exploratory discussions”.
Fine Gael will also hold similar talks with the Green Party this week.
Mr Varadkar, who tendered his resignation as taoiseach (Irish prime minister), last week, said: “The party is willing to engage in exploratory talks with any party that wants to talk [to it].”
The Fine Gael leader will continue as caretaker taoiseach and the previous government will remain in place until a new government can be formed.
It is thought the outcome of Tuesday’s discussions could give an indication of the direction of government formation talks in the weeks ahead.
Four attempts were made to elect a taoiseach last Thursday, with Sinn Féin leader Mary Lou McDonald receiving the most votes.
However, she was still 45 short of the amount required to form a government.
Sinn Féin emerged with the highest number of first preference votes from the 8 February election and won 37 seats, one fewer than Fianna Fáil, which had 38.
On Monday evening, senior members of Sinn Féin called for the formation of a “government of change” at a meeting in Cork attended by about 1,000 people.
Party leader Ms McDonald said the political establishment was trying to stop change.
She rejected claims by Leo Varadkar that such meetings were acts of intimidation, saying it was a “hysterical overreaction”.
Mr Varadkar had said the Sinn Féin rallies were “designed to be the next phase in Sinn Féin’s campaign of intimidation and bullying”.