13% of voters would like to see Minister for Children, Disability and Equality and Kerry TD Norma Foley succeed Micheál Martin as Taoiseach.
The poll in today's Irish Mail on Sunday was based on the responses of 1,000 people canvassed between December 5th and 9th.
Minister Foley has the highest preference from those aged 45 to 54, at 19%, and had a 17% preference among 18 to 24 year olds.
17% of women backed the Fianna Fáil TD, compared to 9% of male voters.
Justice Minister Jim O'Callaghan topped the poll at 36%, followed by Minister for Public Expenditure Jack Chambers, at 20%.