Newly-elected Social Democrats TD Gary Gannon has said he would be "massively uncomfortable" with the prospect of supporting a Fianna Fáil and Fine Gael government.
Leo Varadkar and Micheál Martin will meet early next week for 'exploratory talks' on government formation, as both parties continue to rule out working with Sinn Féin.
The caretaker Taoiseach today said he doesn't know whether next week's talks will eventually lead to a government being formed.
Mr Varadkar said he will report to the Fine Gael parliamentary party whether there is 'any basis' for further discussions once he has spoken to Deputy Martin.
Even working together, Fine Gael and Fianna Fáil would not have the numbers to secure the necessary 81-seat majority in the Dáil - meaning they will require the support of a smaller party and independents to form a working government.
Social Democrats' Dublin Central TD Gary Gannon today told The Pat Kenny Show that he believes the two parties would have the numbers for a majority if they secure the support of the Green Party.
While the Social Democrats - who have six TDs in the new Dáil - have been seen as potential coalition partners in the next government, Deputy Gannon expressed his unease with the prospect of a 'grand coalition'.
He observed: "For me as a new TD... where does that leave me if the only game in town is a grand coalition of Fianna Fáil and Fine Gael?
"From the perspective of the Soc Dems... how does that represent change for the people that voted for me, if all we're doing is going in with Fianna Fáil and Fine Gael?
"I'd be massively uncomfortable to do that. I'd be massively uncomfortable for a variety of reasons."
However, he said he would not criticise the Greens for getting involved in the negotiations for a new government - suggesting Eamon Ryan's party was elected on a "platform of urgency".
Deputy Gannon said: "They can't campaign on ten and a half years of years before ecological destruction, and sit five of them out."
He also said the reasons people went out to vote for Sinn Féin 'have to be respected' - specifically noting their housing spokesperson Eoin Ó Broin's approach to the housing crisis.
'Hostility' in the Dáil
The Social Democrats TD stressed that the next government, whatever form it takes, must focus on tackling the housing crisis and implementing the Sláintecare reforms to the health system.
Speaking about the first sitting of the 33rd Dáil, Deputy Gannon said there was "hostility" in the air in the Dáil chamber.
He said: "We were having the election for Taoiseach, and Micheál Martin had about four pages where he went through a litany of what he considered abuses at Sinn Féin.
"Within all that, we still have to have discussions about the future and what the future of this country looks like.
"There's a massive amount of cruelty and violence that's taken place in this State that still needs to have a truth and reconciliation process towards.
"If we only ever focus on the past, it negates the fact that we still have to build for the future."