And the defender might not be the only Middlesbrough player leaving the Riverside this week, as Rangers will make a formal approach for striker Kris Boyd once Kenny Miller has completed his own move away from Ibrox.
Wheater was not at the Pirelli Stadium on Saturday as Boro were humbled by League Two opponents Burton Albion in the third round of the FA Cup.
Instead, the Redcar-born centre-half was given permission to travel to Lancashire to speak to Bolton officials after Boro accepted an offer for his services on Friday night.
Wolves, Stoke and Everton have all inquired about Wheater, but the Reebok Stadium club are the first to table a bid deemed acceptable to the Boro hierarchy.
Bolton are understood to have offered around £2.5m up front, with a further £1.5m of instalments dependent on Wheater's future performances.
While the 23-year-old was rated closer to the £10m mark during Middlesbrough's Premier League heyday, this month's fee will represent a decent return for a player who is due to become a free agent in the summer.
On Thursday, when he held his pre-match press conference, Mowbray had been intending to include Wheater in the side that played against Burton.
However, the situation changed when an offer was accepted on Friday, and the Boro boss was forced to reluctantly pull the defender from his plans.
Things are happening with David, and that's why he wasn't at Burton, confirmed Mowbray. He wasn't available because of things that were happening behind the scenes.
You never know what might happen still. He's in a delicate situation because every party has to agree.
There's the club that wants to buy him, our club, the player, the player's agent everything has to be right for a deal to happen.
There's still lots of potential for things to change, but David wasn't just sitting at home with his feet up (on Saturday).
He was actively pursuing things and I expect that to continue.
Bolton have had a longstanding interest in Wheater, with boss Owen Coyle insisting any defensive addition during the transfer window will not be a direct replacement for the in-demand Gary Cahill, who is now cup-tied after featuring in his side's 2- 0 win over York City.
Boyd and Gary O'Neil are also cup-tied, after starting at the Pirelli Stadium, but that will not affect the former if he joins a Scottish club.
Tellingly, sources in Scotland claim Rangers boss Walter Smith will attempt to resign the striker once Miller completes an anticipated move away from Glasgow this week.
Rangers accepted Birmingham's offer for Miller on Friday, but the Scotland international is set to snub a move to St Andrew's in order to join Italian side Fiorentina.
Either way, Smith will be looking for a replacement, and after watching Boyd leave Ibrox as a free agent last summer, the Gers boss is hoping to lure the 27-year-old back across the border.
Wages would have been a problem, as Boyd is understood to have doubled his money when he joined Middlesbrough in July. Miller's departure will free up some much-needed funds, however, and Smith is confident of being able to strike a deal acceptable to all parties.
Mowbray has accepted a need to cut Boro's wage bill this month, and as one of the club's highest-paid performers, Boyd is a luxury he cannot afford.
The same could also be true of O'Neil, who is interesting Wolves and West Ham, but does not apply to goalkeeper Jason Steele.
Steele was omitted from Saturday's starting line-up because of a knee injury, not because of a desire to prevent him from becoming cup-tied.
The 20-year-old, who signed a new long-term deal last month, should return for Saturday's Championship game at Bristol City.
Source: Northern Echo
Source: Northern Echo