The 23-year-old, whose contract at Boro expires in the summer, has reportedly caught the interest of a number of Premier League clubs.
Mowbray told the Evening Gazette: "There's very little happening at the moment as far as David Wheater is concerned. Obviously we are fully aware that his contract expires in the summer and we have held talks with David about the situation.
"We know that David wants to play in the Premier League. We would love to think we could give him that opportunity with us as David loves playing for this club he's a local boy and the club means a lot to him. 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. We will wait to see what January brings and whether there are any tempting offers on the table."