Informal talks between Fine Gael and Fianna Fáil on forming a government are likely to begin later today.
Both parties have agreed to hold detailed negotiations, while still continuing discussions with the Green Party.
However, Eamon Ó Cuiv claims Fianna Fáil should form a national government - not a coalition with Fine Gael - because of coronavirus.
Both parties have agreed to hold detailed talks about forming an administration, and they are likely to begin today.
Taoiseach Leo Varadkar previously said he wanted to go into opposition, but now says Covid-19 changes things.
But Galway West TD Eamon Ó Cuiv says many Fianna Fáil TDs are opposed to any coalition with Fine Gael - despite coronavirus.
"It's a crisis that needs to be dealt with and for as long as this lasts, I think there needs to be national unity to get us through this particular crisis.
"Once the crisis has abated, then we have to look at a longer term government, a longer term solution - not a crisis government," he added.
In a statement last night, Fianna Fáil said that "the leaders of Fianna Fáil and Fine Gael have held constructive discussions over the last two days about a series of policy issues and the current political situation. They have decided that teams from the two parties should now commence in depth detailed talks.
They added that discussions with the Green Party will also take place
Additional reporting Juno McEnroe