Ivan Yates said he thinks Leo Varadkar "will win" any leadership contest in the party
The Taoiseach is set to address the issue of his leadership at the Fine Gael parliamentary party meeting this evening.
It is unclear if Enda Kenny will spark an immediate leadership election or delay his departure until later this summer.
The Taoiseach is the third item on the agenda at tonight's meeting - after minutes of last week and matters arising.
Enda Kenny told his colleagues last week he would address what they had been reading in the papers.
While many believe that means he will announce he is stepping down - a move which would spark a leadership contest in the party - others believe he may play for more time and put off a contest until later in the summer.
The reality is that nobody except the man himself knows his plans, and he has remained as coy as ever - even last night, he gave nothing away.
Launching the Nealon's Guide political handbook, the Taoiseach did talk about change being needed if democracy is to survive - but in the foreword of the book, he wrote that his determination is "unyielding".
Ministers Simon Coveney and Leo Varadkar are seen as the frontrunners in any potential leadership contest, with a number of other senior ministers yet to announce whether or not they intend to put their names forward.
Tánaiste Frances Fitzgerald was asked this morning if there should be a third candidate in the race - and she refused to rule herself out.
She told reporters: "There is no vacancy at present - we have to wait and see what the Taoiseach has to say later this evening. I'll make my own position clear then."
Independent TD and Children's Minister Katherine Zappone, however, has given Minister Fitzgerald her encouragement to enter the leadership contest.
She observed: "I think she is a progressive voice within the party, she's a feminist, and I'd be very happy to see her throw her hat into the ring."
Newstalk presenter and former minister Ivan Yates says Varadkar has an early lead in terms of support from TDs and senators.
He observed: "I think we're now at a point, if you were to ask me to name the voting intentions of the 73 members of parliamentary party... I think most people have a good idea about how 60 of them are voting.
"The way I see the campaign developing, is when it eventually does start, there will be a race to get to 40 declarations of support - making it virtually impossible for the other person to win."
He added: "In February I said I thought Leo would win. I think that Leo is not too far off 40 declarations.
"I think Leo has a substantial lead, and I think he will win."
Speaking to Newstalk Breakfast, Ivan also discussed Enda Kenny's path to this evening's announcement.