The defender is believed to have engaged in discussions with the Trotters over a move to the Reebok Stadium after he was pulled out of Boro's squad for the trip to Burton Albion on Saturday.
The situation, after manager Tony Mowbray's admission that things were happening, has alerted other interested clubs over the player's valuation and availability.
Bolton took huge steps towards landing the player, but Everton are now among a clutch of clubs contemplating whether or not to bring forward their attempts to land the 23-year-old.
Everton, Stoke, Wolves and Newcastle who have watched him in the last few weeks have identified Wheater as a target.
Most, however, were prepared to wait until the summer when they would be able to sign the centre-back when he becomes a free agent.
But Bolton's firm move for his services on Friday has alerted the rest of the player's suitors that they will have to act now.
Middlesbrough are believed to be looking for a deal worth around £4m, although the likelihood is that £2.5m is what Bolton would have to pay up front.
But with interest so high, Middlesbrough could find themselves being offered greater terms if the pursuit of Wheater becomes an auction.
Bolton remain the favourites, with the Middlesbrough defender knowing he stands a greater chance of playing under Owen Coyle.
Coyle hinted he would like to sign Wheater, even if the manager's comments suggested there was still some wheeling and dealing to be done before the move is finalised.
Coyle said: He's a very good young player but there's loads of good young players out there. I haven't spoken to Tony Mowbray about David Wheater and people are putting two and two together.
We'd love to bring some players in and help the group we've got. Is David Wheater one of them
I'm not in a position to comment one way or another.
This month is shaping up to be one of the most uncertain in recent years at the Riverside Stadium, where Mowbray needs to trim the wage bill.
Meanwhile, Swansea City remain interested in signing Marvin Emnes this month, but Middlesbrough would not be willing to lose any player unless it suits them.
That means the Swans are unlikely to be able to take the Dutchman on loan for the rest of the season if Boro had to pay a large portion of his wages.
Swansea are keen to bring in another forward after signing Luke Moore from West Bromwich Albion and Boro's Leroy Lita is also thought to be under consideration.
The possibility of Emnes leaving would be reduced if he was going to be ruled out through injury for the next six weeks, which has been speculated.
Emnes had to withdraw from Saturday's trip to the Pirelli Stadium with a foot injury, but Middlesbrough insist he could figure at Bristol City this Saturday.
Barry Robson (thigh) and goalkeeper Jason Steele (knee) were also absent at Burton but they are in contention to return at Ashton Gate.
Boro's home match with Nottingham Forest in the Championship's postponed on Boxing Day has been rearranged to take place at the Riverside Stadium on Tuesday, March 1 (ko 7.45pm).
Source: Northern Echo
Source: Northern Echo