Mowbray's reign at the Riverside is only a few days old but already he faces the prospect of losing the Redcarborn defender.
The captain's contract expires at the end of this season with an agreement yet to be reached over a new deal.
Wheater turns 24 in February, which means he could leave the Riverside for nothing in the summer as the Bosman ruling dictates a club is due no compensation after a player reaches 24.
This isn't the first time Boro have been in this position after Ross Turnbull left on a free two years ago.
Like Wheater, the goalkeeper came through the Academy at Middlesbrough, but after failing to sign a new contract he joined Chelsea for free after turning 24.
While Mowbray insists Wheater is an important part of his plans, he admitted he would not stand in the defender's way should he decide his future lies elsewhere. But he reiterated his desire to keep the defender.
I hope he will be an important part, Mowbray said.
The contractual situation is what it is with David and it's not something I've looked at.
But I have spoken to him and told him how much I appreciate his talent.
I like what I see and hopefully we can resolve the situation as soon as possible.
He's a big asset for the club and we need to try and protect that asset, but if we do have to let him go we must make sure we get some value.
Talented players deserve to play right at the top of the tree, and when we are struggling at the bottom of the Championship who are we to stand in his way
But all I can do is express my appreciation of his talent and hope that he sees an opportunity to give me and the club time to achieve where he wants to be playing at.
Despite the issues surrounding Wheater's future, Mowbray revealed his excitement at the prospect of working with the captain and revealed he can already see the the defender's quality.
Of course I am looking forward to working with him,
said the former West Brom boss.
I can see already in the first few days he's very commanding and he knows his job.
Everybody tells me he went through a sticky patch last year, but he looks on the ball to me and very confident and assured.'' Boro face bottom club Bristol City at the Riverside today in Mowbray's first game in charge and the new manager has asked fans to be patient and not to expect too many changes straightaway.
It is a long process, the former Boro captain said.
Supporters hopefully won't expect to see any massive changes, it will be same players and hopefully with a few more supporters through the door, they will be trying to impress.
Hopefully the positive affect of a new manager will turn it into a victory for us.
Mowbray who revealed his starting XI to his players yesterday admitted he was looking forward to walking out as manager for the first time and hopes an improved atmosphere can help spur his side on.
I try to be as professional and organised as possible and it is great if fans are there because of a change of manager,'' he said.
They must be getting on if they remember me as a player, because it was 20 years ago, but it is important the crowd are up for the game.
I always remember them trying to suck the ball into the net and that is what we need to try and achieve a positive result.
I am not thinking promotion, I am thinking about winning the first game.
Successful teams in this league are ones in a confident mood who find a level of consistency.
That is what we will strive to do in the first game and then get on a roll.
Source: Northern Echo
Source: Northern Echo