Minister for Housing Simon Coveney has said that all Fine Gael ministers are very busy and his focus is on the work he needs to do in his department.
Speaking at UCC this afternoon, Mr Coveney said he is not getting into a formal Fine Gael leadership pitch when there is no contest under way.
A leadership contest is a distraction at this time, he said, adding that his focus is on his ministerial brief.
Taoiseach Enda Kenny has said he intends to address the issue of his leadership shortly after his return from Washington for St Patrick's Day celebrations next month.
Mr Coveney said he has full faith in Mr Kenny's ability to manage what will be a very important transition for the country.
He said he has been through some leadership changes in Fine Gael which have almost "ripped the party in two", but said he is determined that will not happen this time.
Minister for Social Protection Leo Varadkar earlier said conversations about the Fine Gael leadership "are happening".
He also said an election would not be good for the country. He was responding to a question as to whether a change in the party's leadership would trigger an election.
He said the Programme for Government stands, irrespective of who is Fine Gael leader.