No Taoiseach nominee is expected to win a Dáil vote
The outgoing Tánaiste and Labour leader has called for Fianna Fáil and Fine Gael to work together to provide the country with a stable government.
Joan Burton was speaking in the Dáil on nominations for Taoiseach.
But neither Enda Kenny, Micheál Martin, Gerry Adams or Richard Boyd-Barrett are expected to get a majority.
This will result in Mr Kenny's resignation as Taoiseach, but he will continue in a caretaker capacity.
Then all eyes will turn to Fine Gael and Fianna Fáil, to see if they can hammer out a deal and enter a grand coalition in the coming weeks.
Ms Burton says there is only one solution now to provide government.
And the call for a Fine Gael-Fianna Fáil government also came from the Green Party.
Leader Eamon Ryan says his grandparents proved it could work.
Fine Gael are officially the largest party with 50 seats, while Fianna Fáil are the second largest with 44.
Meanwhile, a former Minister and Fianna Fáil TD says it might be time for Enda Kenny to step down as leader of Fine Gael.
Mary O'Rourke thinks it might be the key to a successful partnership government between Fianna Fail and Fine Gael.
"I think the personalities of Micheál Martin and Enda Kenny couldn't be further apart, but needs must if the devil drives".
I don't know, because MM said he would not go in with with Enda Kenny and Fine Gael".
So perhaps somebody can change leaders, and it's not Fianna Fáil", she added.