"He's a good player and he'll always be linked with moves and I'm sure lots of the Turkish clubs would want to take him," Southgate told the Gazette.
"But I'm very happy with what he's done, I enjoy working with him and I don't expect that to be an issue.
"I think Tuncay's enjoying his football with us, I think he's improved as the season has gone on.
"He's enjoying life here as well, he's a very happy lad who enjoys his work and I think he's been an asset for us this season and one we would certainly not want to lose."