Leo Varadkar and Micheál Martin have spoken about the future of the confidence and supply arrangement.
The two political party leaders spoke by phone yesterday evening in the wake of the final budget of the existing deal.
Their officials are to talk about putting a process in place to further discuss the arrangement.
Taoiseach Leo Varadkar wants the deal extended until 2020, while Micheál Martin has so far only spoken about reviewing the current arrangement.
However, the Taoiseach has also indicated he wants any new agreement finalised by Halloween.
Many in Fine Gael are itching to take advantage of good poll numbers with a November election.
In Fianna Fáil, meanwhile, some think the party would gain nothing by renewing the deal that's kept them in a kind of opposition limbo over the last few years.
The confidence and supply arrangement is now likely to dominate the conversation in Leinster House over the coming weeks and months.
For a brief guide of where the government plans to spend it's money next year, check out Today FM's Budget 2019 Breakdown