There's growing optimism that Fine Gael and Fianna Fáil will reach a deal allowing a minority government to be formed.
Negotiators on both sides say work remains to be done, but Fine Gael sources believe a government COULD be formed this week.
The parties have almost finished a so-called 'framework document', but discussions on policy areas still have some way to go.
Discussions on those issues will resume today - with Irish Water remaining a key sticking point.
But figures on both sides have acknowledged that the 'framework document', which will underpin the general 'architecture' of a minority government and how Fianna Fail will allow it to take power, is virtually complete.
The Dail is due to reconvene tomorrow for two days of debates on a range of issues, which was due to include a session of statements on agriculture on Thursday afternoon.
But the latter debate has now been cancelled - potentially clearing the Dail schedule to make way for the election of a Taoiseach.
Our political correspondent Gavan Reilly filed this report for Today FM's National Lunchtime News: