As reported by Sky Sports, Chelsea and Arsenal have been leading a whole host of European clubs interested in snapping up the talented Turkish international at the end of the season.
Liverpool, Juventus, and Atletico Madrid have all been linked with Calhanoglu, alongside Chelsea and Arsenal.
But Hamburg have moved early to warn off the potential suitors, as Kreuzer told Hamburger Morgenpost that he's not willing to entertain any offers for Calhanoglu.
"Selling Hakan is definitely not an option," said Kreuzer.
The 20-year-old forward has ten goals in 28 appearances for struggling Hamburg this summer, after returning from a successful loan spell with Karlsruher SC last season.
He recently penned a new contract that keeps him at the club until the summer of 2018, and his agent, Bektas Demirtas, has confirmed that his player is not interested in leaving the imtech-Arena anytime soon.
"We have not been receiving official enquiries from any club with regard to Hakan's future," he said. "Nothing serious, no single club.
"There is also no reason as Hakan wanted to sign a long-term deal at Hamburg in February. He feels at home at the club. Any action is therefore up to the club.
"We would only start considering if Hamburg start negotiations with another club."
Calhanoglu has one international cap for Turkey although he was born in Germany.