The 22-year-old has been a long-term target for Tottenham, who have been rebuffed on several occasions, while reports over the weekend suggested Everton have made his capture a priority.
However Boro manager Gareth Southgate, who has already lost striker Mark Viduka to derby rivals Newcastle, was quick to issue a hands-off message.
He told the Boro website: "Stewart is such a good player and is now an established player in the England squad, so I am not at all surprised that other clubs might be interested in him, but that's as far as it goes.
"Stewart is definitely not for sale, so other clubs would be wasting their time even considering making an offer.
"The idea that we would want to sell the likes of Stewart is way off target."