Based on yesterday's and today's declarations, Mr Varadkar has established a lead within the parliamentary party but those campaigning for Minister for Housing Mr Coveney say a significant number remain undecided.
TAOISEACH ENDA KENNY is to retire as Fine Gael leader, and step down as head of government.
Kenny received a standing ovation from his colleagues and was described as "very emotional" by those present.
Questions will immediately turn to a successor and Ireland's next taoiseach alongside the analysis of Mr Kenny's legacy after leading the country out of a crippling recession, albeit with an agenda of austerity.
Enda Kenny, who announced his resignation after 15 years as leader and six as taoiseach, said he will carry on his duties until then.
"I thank all our members, past and present, for that privilege".
Kenny tweeted a statement as that meeting began, confirming his plans, ahead of the news being leaked in other ways.
As of last night, the Social Protection Minister had secured nearly twice as much support of the Fine Gael parliamentary party as Coveney.
"But more importantly he brought this country back from the brink of economic collapse, and offered political stability when countries across Europe were staring into the abyss".
Another senior member said: "The body language of some of his loyal supporters said it all, there were a few teary eyes".
Ms Fitzgerald decided against standing for the leadership, as did Minister for Education Richard Bruton, who immediately said he would be supporting Mr Varadkar.
Mr Donohoe's support is also significant, as he is one of the most influential members of the Cabinet and has been tipped as a potential minister for finance once Michael Noonan steps down after the leadership race.
At the Fine Gael parliamentary party meeting, participants gave a long standing ovation to Kenny, praising him for his remarkable service to the country and party.
Irish Prime Minister Enda Kenny speaks to the media at the general election count centre in Castlebar, Ireland February 27, 2016.
When asked about comments Mr Varadkar made in 2015 that he would stay in politics for another 15 years, he said he was not sticking to that timeline.