Tony Mowbray is much-loved by Middlesbrough fans

Boro chief executive Keith Lamb had earlier hinted that Mowbray would be in the running to succeed Steve McClaren at the Riverside.

But Mowbray told BBC Scotland: "People are making a natural connection, but I just want to get on with my job here."

But he conceded: "I'm ambitious and I want to manage at the highest level."

For the moment though, Mowbray is looking ahead to next season at Easter Road.

"We had another good season and competed well with teams who have a lot more resources," he added.

"I'm concentrating now on building for next season. We know which players are definitely going and there are gaps to fill."

Nonetheless, he is likely to be a candidate when Middlesbrough begin to consider replacements for McClaren in earnest when he leaves on 16 May.

Lamb told BBC Sport on Saturday: "I'm not ruling anyone in or out. But I know Tony well.

"I speak to him quite regularly. I am also well aware of how well he has done and, when the time's right, we'll sit down and look at things."

McClaren will replace Sven-Goran Eriksson as England coach next season and will lead Boro for the final time in the Uefa Cup final on 10 May.

Former Celtic manager Martin O'Neill is believed to be the strong favourite for the Boro job.