Enda Kenny has said he will deal with the issue of leadership after St Patrick's Day
Simon Harris has ruled himself out of the running to become Fine Gael's next leader.
The Health Minister admits he "does not have enough experience at present".
In recent weeks, Harris had refused to rule himself out of the contest - saying his young age should not disqualify him from being considered.
Speaking on RTÉ this morning, the 30-year-old Health Minister said he is "flattered" to have been linked to the role - but added he has a busy portfolio to deal with.
Enda Kenny has indicated he will deal with the issue of his leadership after St Patrick's Day and his visit to Washington.
Social Protection Minister Leo Varadkar has said he will campaign in the event of a leadership contest, while Housing, Planning, Community and Local Government Simon Coveney is also expected to run.
Several other senior ministers have not yet ruled themselves out of any contest.
A poll this weekend showed that nearly half of Fine Gael voters would favour Simon Coveney over Leo Varadkar as party leader in a head-to-head to race - but Varadkar would have the edge in a contest with multiple candidates.