Social Protection Minister Leo Varadkar commands a modest lead in terms of support within the parliamentary party.
While supporters of both Mr Varadkar and Simon Coveney present different pictures in terms of their level of support, an analysis by this newspaper shows the Dublin West TD to be ahead. The electorate for the Fine Gael contest is split on the following grounds: parliamentary party (65pc), rank-and-file members (25pc) and councillors (10pc).
This means that securing the support of the majority of TDs, senators and MEPs is crucial to the outcome.
According to declarations to date, Mr Varadkar is ahead in terms of the parliamentary party.
His known supporters include junior ministers Eoin Murphy and Seán Kyne, TDs John Paul Phelan, Noel Rock, Michael D'Arcy, Josepha Madigan, Pat Deering, Jim Daly, Tom Neville and Brendan Griffin, and senators Neale Richmond and Catherine Noone.
Others expected to publicly back Mr Varadkar include ministers Paschal Donohoe, Paul Kehoe and Joe McHugh, as well as Galway deputy Ciarán Cannon, Brian Hayes MEP and senators Martin Conway, Frank Feighan, Maria Byrne and Ray Butler.
While Mr Coveney has fewer declared supporters within the parliamentary party, he is known to have won the backing of Health Minister Simon Harris.
Junior ministers Damien English and Dara Murphy are leading figures in his campaign, along with TDs Kate O'Connell, Maria Bailey and senators Tim Lombard, Paudie Coffey and Jerry Buttimer.
He is also believed to have the support of the party's MEPs, Deirdre Clune, Seán Kelly and Mairead McGuinness.