Asked whether he would like to lead the party, he replied that it was not going to happen "any time soon" with Taoiseach Enda Kenny in charge.
In an interview, he said he wanted to devote all his energy to his job as Agriculture Minister, driving growth in the sector.
"My focus very much is on my own department and I hope that I can stay here long enough to make an impact."
It is understandable that he does not want to talk about the leadership, given that it is less than two years since he was involved in an unsuccessful heave against Mr Kenny.
He has had a successful stint in his department, helped by the upturn in global food prices and agri-business – and by his own enthusiasm.
Mr Coveney said progress on opening up Chinese and US markets to Irish beef will be made in the next 18 months. There was a very good relationship with Chinese officials.
"I think we need to be patient and respectful. They have real concerns around consumer health and BSE."
Mr Coveney said he expected farmers would pay the forthcoming property tax without Revenue having to resort to docking their single farm payments.
"I don't think there is going to be a big enforcement issue here with them. They are a community that do pay their taxes and do respect the Revenue," he said.
One of his most significant pieces of forthcoming legislation is the animal welfare bill, which will impose €250 out-of-court fines for animal cruelty, as well as lifetime bans on ownership of animals.
"When you listen to some of the stories in terms of abuse and neglect of animals by people who should never be near animals, then I think we have an obligation to deal with that," he said.
Mr Coveney promised that the heavy penalties in the bill relating to illegal dog fighting – which make it an offence to even attend a dogfight – would help stamp it out.
"Anyone who has dogs at home, it makes them sick to their stomach to think of dogs ripping each other apart for entertainment purposes," he said.
There are concerns about the Government's plans to include the harvesting rights to Coillte's trees in the sale of state assets. But the minister insisted the public will not lose access to forests.
"If we sell harvesting rights to trees, we're not selling the land and we will be protecting the public good elements of Coillte. A lot of the broadleaf forests will not be cut down and there will be public access and bike trails and so on.''
Mr Coveney has been pushing for the new online betting tax of 1pc, due to be introduced in the first half of 2013 to provide funding for the horse and greyhound industry. The Government has been propping up the fund for these sports to the tune of €25m per year due to the fall in betting tax revenue.
The new online betting tax would bring in €15m extra in a full year.
"I think that's a start. And then we can have a debate about whether we can increase the actual rates to bring in more revenue," he said.
The country needed to protect its competitive edge in the €1.5bn horse racing industry, which employs 27,000 people.
"Ireland is better at horse racing in terms of breeding, training and jockeying than any other country in the world. If we ever lose that edge, we'll never get it back again," he warned.