Health Minister Simon Harris has ruled himself out of running for the Fine Gael leadership but refused to say who he will back in the race,
.Mr Harris said he had a lot of work to do as the minister for health and therefore was not contesting the post - when it becomes available.
Taoiseach Enda Kenny has said that he will give conclusive details about his position after St Patrick's Day, following recent calls for him to set a resignation date.
Mr Harris, speaking to Sean O' Rourke on RTÉ Radio 1, said he was flattered to be asked by a number of people but the time was not right for him.
He said he had a challenging ministry to deal with and he did not have the experience for the role.
Mr Harris said he was ambitious for his party and country and he was ruling himself out to end any distraction.
He declined to say who he would back for Fine Gael leader but said once the Taoiseach announced he was stepping down, he would announce who he would support for leader and that he would campaign for them.
The Health Minister said that he did ask Cystic Fibrosis campaigners to call off a demonstration for the drug Orkambi but said it was not to be disrespectful.
Mr Harris said he thought long and hard before making the request.
Mr Harris said the government was close to reaching a deal on Orkambi and another drug, Kalydeco, and he didn't want to jeopardise that.
He said he hoped to make an announcement in the next few weeks.