Enda Kenny is expected to clarify his leadership intentions this week
Three Fine Gael Ministers have refused to rule themselves out of a potential leadership race in the party.
Simon Harris, Frances Fitzgerald and Richard Bruton have yet to declare their intentions.
Enda Kenny is expected to clarify his plans as leader of Fine Gael - and Taoiseach - later this week.
Over the weekend, WhatsApp messages from within the party appeared to suggest the Health Minister could enter the race.
Minister for Foreign Affairs Charlie Flanagan posted a message in the group on Sunday morning saying: "[Simon Harris] hasn't announced yet but Frances is encouraging him. He wants out of Health."
Minister Flanagan later described his comments as "tongue in cheek".
The leaks prompted Minister Harris to tweet that he has 'no intention of engaging in idle speculation'.
However, speaking earlier today he refused to rule himself out of a potential leadership race.
He said: "[Enda Kenny] has my full confidence and support. If and when a vacancy arises in the Fine Gael party, I'll consider my options at that stage - as I'm sure many other colleagues will also."
Speaking at a conference taking place in Dublin earlier today, Education Minister Richard Bruton was asked repeatedly if he would run for the party leadership himself - and did not rule himself out.
"At this point there is no vacancy - I'm not commenting on any of the contenders," he said.
Tánaiste Frances Fitzgerald says she wants to wait until after this week's parliamentary party meeting on Wednesday.
"It's very important we wait and hear what the Taoiseach has to say," she said.
Minister Leo Varadkar has now reportedly shut the parliamentary party's WhatsApp chat down in favour of a secure messaging app called 'Confide', which supports auto-deleting messages.
Meanwhile, Minister Varadkar and Simon Coveney - seen as the two most likely leadership candidates - agree Enda Kenny should remain as leader until after his St Patrick's Day trip to the White House.
Kevin Doyle is Group Political Editor of the Irish Independent, and he spoke to Newstalk Breakfast about the situation as it stands.
"The writing is on the wall for Enda Kenny," he explained. "He knows if he doesn't give some sort of indication of what his intentions are come Wednesday, an all-out split within the party could emerge.
"It's likely there'd be a motion of no confidence put down, because there are people on the backbenches who have become increasingly worried the longer Enda Kenny stays, the less chance they have of re-election. And all the time that election is getting closer and closer," he added.
Michael O’Regan, Parliamentary Correspondent with The Irish Times, told Jonathan Healy on The Pat Kenny Show that the Fine Gael leadership contest will be a three-week campaign about the future of the party and its future in Government.
"It also, of course, will be about the election of a Taoiseach, which makes it a slightly different leadership campaign than it might have been otherwise," he observed.
"The feeling around Leinster House is that a longer campaign would suit Simon Coveney, that he might come from behind so to speak. I think at the end of the day that Simon Harris won't run, I think Frances Fitzgerald probably won't win. Then you have Coveney vs Varadkar... a three-week campaign, anything could happen."