The 25-year-old, who joined from Hungarian side Gyori ETO in August last year, has been the subject of a series of enquiries as Boro attempt to re-shape their squad.
But having sold David Wheater to Bolton and Gary O'Neil to West Ham and amid interest from Russia in striker Kris Boyd, Mowbray is determined to hang on to Kink.
He told the club's official website: "I have had a few enquiries about Tarmo but he won't be leaving.
"He has a very obvious talent but he has to learn and understand the mentality that's needed to be a success in the Championship.
"To be fair, he wants to prove he can be a success here and I'm happy to give him that opportunity."