Independent TD Michael Lowry has predicted that Mary Lou McDonald will be elected taoiseach next Thursday when the 33rd Dáil meets for the first time.
The former Cabinet minister - who has previously given his support to Fine Gael and Fianna Fáil governments - believes that the two parties will be instrumental in the formation of the next government.
Speaking on RTÉ's Prime Time, Mr Lowry said: "The people are saying that they want Mary Lou and Sinn Féin. So give them the opportunity to see if it is possible to form a government.
"I believe that it is possible for them to start the initial steps. I think it is possible for her to become Taoiseach next Thursday, which many people would never have predicted but I think that's possible."
But the Tipperary TD is pessimistic about the prospects of a left-leaning government getting off the ground.
He said: "She then has to go and form a government and form a policy platform. She has to come back to Dáil Éireann and I think that is where that will come crashing down."
Mr Lowry, who was elected for the ninth consecutive election last weekend, acknowledges that the "political landscape has changed dramatically. And there are a lot of turbulent days ahead. I feel myself that it is quite possible that Mary Lou will become Taoiseach next Thursday."
But he added: "Then she will be asked to form a Government. I think she will come back with a weak government with a policy platform that will not get support from anyone outside the left socialist wing of the Dáil.
"And then I would imagine that after that she would have to go back to the Áras. I can't speak for the President but I doubt in those circumstances that he would allow for dissolution of the Dáil.
"And the inevitable then would be that the only people that can form a government would be Fianna Fáil and Fine Gael with the support of the Greens or a group of Independents.
"I think that there will be a lot of pandering, talking, to-ing and froing but ultimately it is going to come back to that," he predicted.
"The warning signs have been given to both Fine Gael and Fianna Fáil that they have not performed to the extent that the people expected of them. I do believe that they have the capability and the ability to turn it around."
Mr Lowry expects that around 15 Independent TDs will "come into play" yet before a government is formed.