Middlesbrough boss Gareth Southgate has issued a hands-off warning to Fenerbahce and Galatasaray after the Turkish duo were linked with Tuncay.
Reports over the weekend suggested the two Istanbul giants were preparing £5million offers to try and take Tuncay back to Turkey.
But Southgate says there is no way Tuncay - who arrived at the Riverside last summer on a free transfer - will be leaving.
He said: "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 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."
After struggling to adapt to life in England at first, Tuncay insists he is now more than happy with life on Teesside.