Micheál Martin has reportedly informed Enda Kenny that there will be no 'grand coalition' between Fianna Fáil and Fine Gael.
The Sunday Independent reports that the Fianna Fáil leader would be happy to have a second election, rather than take his party into government with Fine Gael.
The newspaper also reports that Acting Taoiseach Enda Kenny is seeking to break up the Independent Alliance by offering some members Cabinet positions.
There is growing speculation that Michael Healy-Rae could be offered the job of Minister for Rural Affairs in exchange for his support of a minority Government.
Independent Mattie McGrath, who is being courted by Fianna Fáil and Fine Gael, said that the two big parties should get down to the business of forming a grand coalition.
"This is very, very concerning," he said.
"I think the two main parties must be, I won't say forced, but kind of gently coaxed along to go into talks in the interest of our electorate, and our people, and debt forgiveness and many other issues - the housing crisis and health crisis.
"So we need to have these bigger parties that have the larger share of the votes, they really need to come to their senses and engage with each other immediately."