The Labour Party remains fundamentally divided on the merits of joining the next Government.
With 87 seats between them, Fianna Fáil and Fine Gael are within touching distance of a majority in the next Dáil.
Despite this, the two parties would like a third to join them in coalition - to protect the Government’s majority against any future defections or by-election defeats.
Both Fianna Fáil and Fine Gael have spent time in coalition with Labour before and Tipperary North TD Alan Kelly said he is "quite open" to an offer from them.
"There's no point in standing on the sidelines, you've got to consider going on the pitch and play," he told RTÉ.
By contrast, his newly elected colleague in Dublin Central, Marie Sherlock, said that with only 11 TDs, Labour would not have the influence to make significant changes in Government.
On Newstalk Breakfast, party member Fergus Finlay, who has been involved in the party since 1981, said there is no need for them to join the next Government.
“On a number of occasions in that time, we’ve had to go into Government,” he said.
“There were always two pressing reasons; one was that no Government was possible without Labour’s participation - because of the numbers in the Dáil.
“The other one was that there was a terrible mess to be cleared up. Neither of those reasons exist right at the moment; nobody needs us in Government.
“Fianna Fáil and Fine Gael don’t need us in Government - they’d like us in Government.
“They’d like us in Government because they look at us and they think we’re responsible, we’re decent, we’re long haul kind of people and that would make life easier for them.”
Mr Finlay also said the gap between Fianna Fáil and Fine Gael and the Labour Party is too wide on a number of important issues.
“I think there are massive differences in terms of foreign policy - in terms of militarism and so on,” he said.
“I think the fundamental difference is around housing; everyone talks about building oodles and oodles of social and affordable housing - where the hell are they?
“The parties that have been in power for a long, long time now have failed catastrophically to address the housing issue.”
Left-wing alternative
Both the Labour Party and the Social Democrats won 11 seats and Mr Finlay hopes the two parties can work together with a view to eventually replacing Fianna Fáil and Fine Gael in Government altogether.
“I believe Labour and the Social Democrats, working together on the basis of respect and equality, have a real chance now to begin rebuilding the Social Democratic project - which has become pretty moribund,” he said.
“Not just in Ireland but throughout the world.
“Labour should stay out and, in the next five-years, be part of rebuilding something that is radically different in Ireland.”
If the Labour Party does not join the Government, it is likely Fianna Fáil and Fine Gael will seek to do a deal with “sensible” independents.
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Main image shows Labour leader Ivana Bacik with Labour candidate Senator Marie Sherlock at the count centre in the RDS. Photograph: Leah Farrell / © RollingNews.ie