The home-grown defender had been tipped to leave The Riverside last summer after Boro's relegation from the Premier League, only to stay for the club's disappointing Championship campaign.
He now has just 12 months remaining on his contract and is again likely to attract interest from clubs in the top flight over the coming weeks - with Bolton and Wigan reportedly ready to lock horns for his services.
The 23-year-old, who has made over 130 appearances for Boro, is keen to stay on Teesside and aid the club's bid for a return to the Premier League next season.
However, he is also aware that any need to bring in extra finance could lead to him being sold during the transfer window.
"I've always said I'm happy to stay and I wouldn't ask for a transfer, but it's for the manager, Keith Lamb and the chairman to sort out, really," Wheater told the Evening Gazette.
"I've got a year left, so I'll see what happens in the summer.
"Obviously, if I'm here I want us to get promoted, but you don't know where you're going to be with the way football is at the moment, clubs need cash.
"Obviously, I've got a year left so I'll definitely be back for pre-season. This is my club so I'm going to try my hardest, until I leave."