Taoiseach Enda Kenny has told the Fine Gael parliamentary party that he will address the leadership issue at the parliamentary party meeting next Wednesday.
At a meeting of the parliamentary party last month, Mr Kenny said he would deal with the leadership issue after the 29 April EU Council meeting.
He also told members there would be an orderly transition.
Mr Kenny, though, was unable to address the issue last week as he was travelling to Canada.
If Mr Kenny resigned as party leader tonight, a leadership contest would officially begin tomorrow.
That would coincide with EU Brexit negotiator Michel Barnier's address to a joint sitting of the Dáil and Seanad in the morning.
Although the contest has not officially begun, there is intensive campaigning under way by Minister for Social Protection Leo Varadkar and Minister for Housing Simon Coveney.
It is not yet clear if there will be other candidates once the vacancy is officially confirmed.
Mr Varadkar this morning said he did not expect Mr Kenny to address the leadership issue at today's meeting.
Varadkar has "no idea" when Kenny will step down, but is "totally zen" about it pic.twitter.com/vHIfw0D0RM— RTÉ News (@rtenews) May 10, 2017
While pointing out there is no vacancy, he said the context has changed in the past few months given the fact the Taoiseach has indicated he will step down.
The minister said, however, that he has been talking to colleagues, councillors and party members even though there is no formal campaign under way.