Justice Minister Frances Fitzgerald has indicated she may contest for the Fine Gael leadership after Enda Kenny steps down.
Mr Kenny has previously indicated the next General Election will be his last as party leader, and Minister Fitzgerald said she was not ruling herself out of the contest.
She said did not want to speculate about the leadership, as no vacancy existed currently for the role.
However, she said in an interview with the Sunday Independent that she has "always enjoyed leading" in her various political roles.
Leo Varadkar and Simon Coveney are seen as the two others contenders for the party leadership.