A new poll shows Simon Coveney is the favourite among ordinary Fine Gael members to take over the party.
Leo Varadkar, his rival to replace Enda Kenny, has so far had more support from Fine Gael Ministers.
But the latest stats from the MRBI Irish Times survey claim 48% of regular Fine Gael voters would like Coveney, over 44% for Varadkar.
The poll was conducted on Tuesday and Wednesday of this week - before last night's first regional debate between the two candidates.
The husting in Dublin attracted hundreds of Fine Gael members who heard Coveney and Varadkar take aim at each other over their eagerness to become leader.
Meanwhile Fine Gael party faithful will have another opportunity to hear from Ministers Coveney and Varadkar tonight.
The second husting takes place in Carlow.