The Taoiseach Leo Varadkar says Fine Gael will wait until President Michael D Higgins announces his intentions before deciding whether to field a presidential election candidate.
Mr Varadkar's comments come after Junior Minister Finian McGrath said there is a "cosy consensus" not to contest the election if the President wants a second term.
Fianna Fáil has already confirmed they will not field a candidate if President Higgins runs again.
The Taoiseach has said they are waiting to decide.
He said: "It's really up to candidates to come forward and seek nominations if they wish to.
"As far as Fine Gael is concerned, and speaking as leader of Fine Gael, we'll make a decision when President Higgins makes his announcement as to whether he's nominating himself for a second term as an independent.
"That's obviously a decision he'll make in the coming weeks and we think the respectful thing to do is to wait for him to do that first before making a decision ourselves."