The Turkey international, who has also been linked with Chelsea and Manchester City, has scored five goals in 18 appearances for Bundesliga strugglers this season.
"I always said that I'm happy in Hamburg and with HSV. I would like to play for this club in the Bundesliga for a long time yet and I want to become a regular in the team," talkSPORT quotes him as saying.
"I also wanted to make a statement in our difficult situation."
Calhanoglu is now under contract at Hamburg until the summer of 2018.