Press Association Sport understands that discussions with the 23-year-old, who is out of contract at the Riverside Stadium at the end of the season, are at an advanced stage.
Boro boss Tony Mowbray has all but accepted that he will have to sell Wheater, rather than lose him on a free transfer at the end of the campaign, to help generate funds for the rebuilding work he wants to do this month.
The Redcar-born player has been a fixture in the Boro side in recent seasons since emerging from the academy and at one stage fought his way to the fringes of the England squad.
Source: PA
