Social Protection Minister, Leo Varadkar, and Housing Minister Simon Coveney are the only two contesting
The Barrow centre at IT Carlow will host the Carlow hustings.
A decision on the successor is expected by June 2nd.
John Murphy was speaking ahead of Fine Gael's Parliamentary Party Meeting this evening
Enda Kenny signalled that he would make a decision after his trip to the White House for St Patrick's Day.
There's been renewed pressure on Enda Kenny to step down as leader of Fine Gael