Senior figures in Fine Gael and Fianna Fáil have dismissed any suggestion of a coming together.
It follows comments made by the broadcaster and former Fine Gael strategist Bill O'Herlihy at the annual Michael Collins Commemoration at Béal na Bláth in West Cork.
He called for an end to civil war politics and a coalition between the two parties.
But tonight Fine Gael sources said it was not an issue and the party's focus is its work in government.
Fianna Fáil sources said their priority remained rebuilding the party.
In his address earlier today, Mr O’Herlihy said he believed such a coalition had much to offer at a time of huge challenge for Ireland and would represent a sea change in Irish political life.
He added that it would be an "enormous challenge to implement", but he believed people would like to see it happen.
Mr Herlihy said he recognised the fear people would have of an overwhelming political majority, the distrust the electorate had of the last Fianna Fail administration and the determination they had that this would not be allowed to happen again.
He said recent political events had reversed the shape of Irish politics and had left Fianna Fáil competing with Labour and a renewed Sinn Fein for space in the centre-left ground.