Boro sold the centre-half to Bolton Wanderers in January 2011 and would reportedly welcome the opportunity to return him to their ranks.
They are, however, working to a tight budget at the Riverside Stadium and are in no position to finance a deal.
Wheater only has 12 months left to run on his current contract at the Reebok Stadium, but reports suggest that he could be offered fresh terms by Bolton.
Taking that into account, Mowbray admits there is no chance of putting a deal in place for the 26-year-old defender.
On the Wheater rumours, he told the Gazette: "I don't know anything about that, I don't know where that's come from.
"The reality of that is it doesn't fit in with where we are as a football club at the moment knowing what David was on salary-wise when he left us to what he would be going to at a Premier League club.
"To come back to us, I can't see how that can happen and it's not something we've considered."