Fianna Fáil and Fine Gael may ask the Dáil to postpone voting on a Taoiseach this week.
Both parties' negotiating teams held their first talks last night - to assess how a minority Government would work.
They are due to meet again today and described their first meeting as constructive and cordial.
The two parties have agreed not to reveal details of their negotiations.
Meanwhile, employers group IBEC says the economy needs a strong stable government in place as soon as possible.
The business group says the political situation is already having an economic impact.
IBEC's director of policy Fergal O'Brien thinks the uncertainty is a factor in falling consumer confidence: