A senior cabinet minister, Fine Gael's Simon Coveney, says he would have an issue with going into government with Fianna Fáil.
Yesterday, the Taoiseach Enda Kenny said he does not "contemplate" doing business with Fianna Fáil, but refused to fully rule out a coalition.
It comes after a number of former Fianna Fáil Ministers indicated they would support a government between the parties.
Micheál Martin says Fianna Fáil will not prop up Fine Gael, but Mr Coveney says Fianna Fáil will not be needed.
The Fine Gael TD said: "I do have an issue with going into government with Fianna Fáil, because I think their record is terrible.
"I don't think we need them back in government and I think we have a very clear proposition for people that can guarantees job creation, continued growth and a very, very good five years of progress for Ireland.
"We can deliver a lot of public services on the back of that economic growth, I don't think that Fianna Fáil can guarantee any of those things."