Leo Varadkar believes he has convinced several influential ministers to publicly back his leadership campaign once the contest formally gets underway.
More than a third of Fine Gael TDs are still viewed as "totally undecided" by the camps of Mr Varadkar and Simon Coveney.
But supporters of Mr Varadkar say he already has some "surprises" ready for when Fine Gael TDs begin publicly declaring their intentions.
It comes as the jockeying for jobs gets under way, with the record number of junior ministers appointed by Taoiseach Enda Kenny last year trying to secure their positions.
Sources say some ministers of state have effectively told Mr Varadkar and his main rival Mr Coveney the price for their vote will be continuing in their ministry.
Sources in the Coveney camp told the Irish Independent they suspect Mr Varadkar has already made "unrealistic promises" of jobs to some TDs.
Sources who aren't linked to either candidate say the contest is "too close to call" but place Mr Varadkar slightly ahead.
The 73 members of the parliamentary party carry the most weight in the election, making up 65pc of the vote. Party members account for 25pc and councillors hold 10pc.
Estimates suggest Mr Varadkar has privately secured the votes of 20-25 TDs, senators and an MEP. Mr Coveney is believed to have a figure in the high teens.
In excess of 25 parliamentary votes are still very much in play. Many of these are junior ministers worried the new leader may try to reduce their numbers, or promote loyal supporters currently on the backbenches. A significant number of party TDs are also reluctant to show their hand before knowing the full line-up of contestants.
Several experienced TDs are arguing behind the scenes that at least one of Paschal Donohoe, Frances Fitzgerald or Richard Bruton should enter the fray to prevent a divisive head-to-head between the two young guns.
The Taoiseach is to signal his departure date after St Patrick's Day, although Foreign Affairs Minister Charlie Flanagan yesterday indicated Mr Kenny will remain working actively on the Brexit issue "for a few months at the very least".
Meanwhile, both Mr Varadkar and Mr Coveney have confirmed they are against sparking a snap general election in the immediate aftermath of the leadership contest.
Mr Varadkar had been viewed within the party as the candidate most likely to go down that route. But he said: "I don't think anybody wants an election, not politicians and not the general public.
"We have an agreement in place with Fianna Fáil based on a confidence and supply arrangement.
"We will honour that - provided they do too...I don't think an election in the short term would serve anyone's interests."
A spokesperson for Mr Coveney said he also doesn't think there should be an election.
"There's a Programme for Government in place and there's a three-year confidence and supply arrangement and that will be the focus of the new Taoiseach," the spokesperson said.
Earlier, Mr Coveney said he believes the party will "stick together" during the leadership contest unlike previous battles, which he said "almost ripped the party in two".
"I don't think that is going to happen this time - certainly I am determined that it won't."