Varadkar is public's favourite to follow Kenny
Acting health minister Leo Varadkar remains the public's clear favourite to succeed Enda Kenny as leader of Fine Gael, according to a Sunday Independent/Millward Brown opinion poll.
Mr Varadkar on 28pc has almost double the support of his nearest rival, acting agriculture minister Simon Coveney at 15pc.
Within Fine Gael, Mr Varadkar is even more popular with 38pc of party supporters saying the would like to see him lead Fine Gael.
This is far ahead of Mr Coveney, who is favourite to lead among just 16pc of Fine Gael voters.
The poll shows 12pc of the public would like to see Mr Kenny remain leader but he has more support within his party where 27pc want him to continue in his current position.
The poll of 865 people conducted between March 21 and April 1 shows 6pc favour acting justice minister Frances Fitzgerald to take charge of Fine Gael - she holds the same level of support within Fine Gael.
Acting transport minister Paschal Donohoe, who emerged as a leadership contender after the General Election, is at 3pc, but this drops to 1pc within the party.
The high-level of support for Mr Varadkar is sure to be of concern to Mr Kenny as he seeks to remain Taoiseach.
However, the minister is understood to be unwilling to move against Mr Kenny in the medium term, despite growing support from both his party and the public for him to take charge of Fine Gael.
Mr Kenny currently has the support of his most senior ministers as talks on forming the next government continue this week.
Senior Fine Gael ministers yesterday ruled out any discussions on Mr Kenny's leadership when they open talks with Fianna Fail.
Speaking to the Sunday Independent, Mr Donohoe weighed in firmly behind Mr Kenny saying there was "no ambiguity" about his leadership and said he has his party's "full support".
And last night, Fianna Fail sources also insisted they will not seek to remove Mr Kenny as a condition for supporting a Fine Gael in government.
This puts Mr Kenny in a strong position to become the first two-term Fine Gael Taoiseach should he secure the support of Fianna Fail for a minority government.
However, there is growing unease about his leadership among his backbenchers and the former TDs who lost their seats in the General Election.
Mr Kenny attended almost every minute of government talks over the past two weeks, which has won him praise from party colleagues and Independent TDs.
However, some senior figures in Fine Gael believe the acting Taoiseach is "overdoing it" in his bid to retain power and is "wearing himself thin".
His supporters also insist Mr Kenny is crucial to the talks with Independents and his chairmanship of the meetings are vital to securing a second term for Fine Gael.
This week, Mr Kenny will brief his parliamentary party on the talks with Independents ahead of a vote for Taoiseach in the Dail on Wednesday.
The outcome of a review of Fine Gael's election campaign which is currently under way will also be crucial to Mr Kenny's future as leader.
Party sources said the external review is at an advanced stage and should be completed by May.