Mowbray has no immediate plans to sell the 23-year-old, who is out of contract in the summer. But the Boro boss revealed a lot will depend on whether any suitable offers are received in January.
"There's very little happening at the moment as far as David Wheater is concerned," Mowbray told the Gazette.
"Obviously we are fully aware that his contract expires in the summer and we have held talks with David about the situation. As far as I am concerned it's a wait and see scenario.
"We know that David wants to play in the Premier League. We would love to think we could give him that opportunity, though the Premier League seems to be some way off at the moment.
"He is ambitious but he is in the same situation as the club as we wait to see what happens over the next few weeks. But we will wait to see what January brings and whether there are any tempting offers on the table."