Boro have been contacted by a number of top-flight clubs in the last ten days to make known their interest in signing him when the transfer window opens in January.
There were also numerous teams represented at Preston North End on Tuesday when Wheater scored the third goal in a 3-1 win to keep Tony Mowbray's men out of the relegation zone.
Wolves, Aston Villa, Newcastle United and Sunderland are believed to be among those thinking about making a cut-price bid for the centreback, although Everton hope to land him for nothing in the summer.
Mowbray has repeatedly acknowledged that Wheater will have to be sold if a suitable offer arrives at a time when the player has been unable to agree terms on a new contract.
However, the 23-year-old claims he will not allow the situation to affect his performances for the club he has graduated through the ranks from during the last ten years.
I love Middlesbrough. I would never say anything else, said Wheater.
I am from this area. If someone else not from the area had the rumours flying around then maybe it might get to them, but I am happy at Middlesbrough so it's a different situation.
You do, obviously, want to play in the Premier League and it is flattering to hear that all of these Premier League teams want you.
But I am a Middlesbrough player until the end of the season, that is when my contract runs to, all I have to do is concentrate on Middlesbrough.'' After the rare away win at Deepdale, Mowbray was quick to pay tribute to Wheater by saying he was a credit to his himself, his family and his friends for the way he has gone about his job.
And the Redcar-born defender, who turns 24 on Valentine's Day, said: It's not difficult for me, definitely not. I don't think of anything else when I am out on the pitch.
When you are out there you don't think of anything other than playing. You forget about your families, everyone, when you are out there playing.
Whatever happens, happens, but when I am out there I just concentrate on the game.
Boro remain firmly embroiled in a fight to climb away from relegation trouble after a win at Preston that leaves them a point adrift of fifth from bottom, Sheffield United, and a point above third bottom Scunthorpe.
But it was nice for Wheater to end 2010 on a high after two years of misery at the Riverside Stadium, when change and three managers have followed relegation.
Wheater said: I have had a countless number of partners, two managers since Gareth Southgate left. Hopefully as a team we can climb up the league.
I don't reflect. I just look forward. If we look back we are looking at bad things really.
We have to look to the future and to brighter days.
Ever since we were relegated, we lost Stewart Downing, Adam Johnson the season after, top players have left.
We should be running away with the Championship so we need to pick it up.
With the new manager the lads are happier with the training, his methods, we are playing a more attacking style, all the lads like him.
If he can make a few signings in January it will be his team and then I think we will do well.