The Turkey international has been strongly linked with a return to homeland since the January window opened.
Galatasaray were reported to be leading the chase for his signature, with Premier League interest from the likes of Arsenal and Liverpool set to be shunned.
Calhanoglu could, however, be about to close the transfer door on all potential suitors.
The 19-year-old is already tied to Hamburg until the summer of 2016, but has now revealed that he would be prepared to prolong that agreement if a suitable offer is put to him.
He told Sky Deutschland: "I am a player of Hamburg. If there is a good new deal, I will happily accept it.
"I would really like to stay on at Hamburg. I want to have a future in the Bundesliga.
"I am sure I will be an even better player in the second half of the season. I am now more used to the standard of competition in this league."