The 22-year-old has been linked with several different Premier League clubs, following Boro’s relegation.
“David’s not for sale,” said Southgate in the Daily Express. “He and Matthew Bates, who has also committed himself to the club, are the types in terms of quality, hunger and desire that we want.
“We have to build our team around those types of characters. We have to make sure the dressing room stays tight through a period that could involve a lot of speculation.
“We wouldn’t welcome bids for David. The key is that he has expressed his desire to stay. The agents that work with him have been very supportive in that and that’s been refreshing for us as well.
“One of the next stages is for him to develop his leadership skills. People look at centre-halves and want good communicators. They want guys with physical stature, but who have leadership abilities, and we have to work at that.
“He has shown his ability and, with experience, that leadership will start to emerge.”