Both Simon Coveney and Leo Varadkar have confirmed they will be campaigning - but are keeping their powders dry for now
One of the frontrunner's to replace Enda Kenny says "very significant surprises" could pop up in the leadership race.
Social Protection Minister Leo Varadkar says talks about the leadership "are happening."
He also confirmed that while he will be campaigning, it has not started yet.
He told Newstalk Breakfast this morning: "I am actually happy in the job I'm doing...whether you believe it or not.
"What I'm doing is the day job and (I'm) very focused on that".
"The campaign for Fine Gael leader hasn't obviously started yet, and when it does I'll be campaigning at that stage".
It comes as the Irish Examiner suggests Housing Minister Simon Coveney has an early lead over Mr Varadkar.
According to an analysis of the 73-member Fine Gael Parliamentary Party, the paper believes Mr Coveney has the support of 37 members, with 30 votes for Mr Varadkar.
But it says six votes are either undecided or too close to call.
Minister Coveney was in Cork today to announce Ireland 2040 – the government’s long-term plan seeking to map out Ireland’s growth for the next 2 decades.
Speaking to Cork’s 96FM he kept his cards close to his chest on the leadership campaign:
“I’m really not getting into a formal leadership pitch at the moment,” he said. “We don’t have a formal process underway.”
“Ministers like me have a lot of work to do in our own briefs and I don’t think we should allow ourselves get down into the distraction of a leadership contest that is not even underway yet.”
Referring to the poll, Mr Varadkar said: "I have to apologise to the general public, they're going to be bored to death with this in the next six weeks.
"There was a poll done by RTÉ of members of the parliamentary party, and that I think had me 2:1 ahead of Simon - so you're going to see endless numbers of these things.
"I think the media will suffer some very significant surprises based on the kind of lists they're drawing up".
Pushed on the issue of the leadership, Mr Varadkar replied: "Inevitably - human nature being nature and politics being politics - I'm meeting my party colleagues all the time...and it doesn't take long for them to bring it up.
"So of course those conversations are happening - but there's no official or formal campaign, and really won't be until after St Patrick's Day".