However, Bektas Demirtas said that Calhanoglu still has a lot to learn at Hamburg even if Arsenal come in for him in January.
"I am aware of an interest of Arsenal in the services of Hakan," he told Hamburger Morgenpost.
"I am expecting Arsenal to approach Hamburger in a more concrete way during this month or January.
"However, Hakan and Hamburger SV, it's a story of success. Our main ambition is that he is staying on with Hamburger SV to progress further as a player."
Calhanoglu has enjoyed a run in the Hamburg team in recent weeks in the absence of the injured Rafael van der Vaart.