The acting Finance Minister Michael Noonan has confirmed that Fine Gael would like to see Labour join it back in government.
Mr Noonan says it is "an open secret" that Fine Gael would prefer to see its former coalition partner back within the fold.
The matter is being considered by Labour TDs, who would need the backing of a special conference to rejoin government.
Speaking ahead of talks between Fine Gael and Fianna Fáil this morning, Mr Noonan warned that a second election was still possible.
Fianna Fáil meanwhile say they will support a Fine Gael/Labour government.
Formal talks between the country's two largest parties on the formation of a new government are resuming.
However, a deal is unlikely to be decided by the next Dáil sitting on Wednesday.
Willie O'Dea, Limerick TD for Fianna Fáil, told Newstalk Breakfast his party will not oppose the deal.
Over the weekend, it was reported that Labour is considering backing Fine Gael in a new minority-led administration.
Tony Heffernan was press and parliamentary director for the Labour Party from 2000 to 2011.
He believes the delay in forming a government is one of the key reasons Labour is now considering going back into power.
Mr Heffernan says it means Joan Burton would avoid a leadership election.
