Varadkar and Coveney are favourites to succeed Enda Kenny
Minister for Health Simon Harris is expected to back Simon Coveney in a FG leadership contest.
Although Mr Harris has refused to comment publicly on his intentions, the speculation within Fine Gael is that he will publicly support the Minister for Housing at a pivotal time in the campaign.
According to a report from The Irish Times, a source within the party said that "Simon will back Simon," before adding "They will wait for the right time so that it can have maximum impact.’"
Mr Harris’s support would be a big boost for Coveney's campaign, given that the Minister for Health is seen as a rising star within the party.
Taoiseach Enda Kenny is expected to announce that he will be stepping down sometime next month.
Leo Varadkar and Simon Coveney are seen as the two favourites to succeed him.
In an opinion poll conducted last month, Fine Gael voters said they would favour Simon Coveney over Leo Varadkar as Fine Gael leader in a head-to-head to race.
The poll showed that 49 % would choose the Housing Minister Coveney, compared to 44% for the Social Protection Minister Varadkar.
In terms of other possible candidates, Tánaiste Frances Fitzgerald and Minister for Education Richard Bruton have yet to publicly declare their intentions, while Minister for Public Expenditure Paschal Donohoe has ruled himself out.
Mr Donohoe may well be the next minister for finance if, as expected, current Minister Michael Noonan stands down when Mr Kenny departs.