The 21-year-old Dutch centre-back, who is currently on loan at the German side, insists that negotiations have started to extend his stay at the Imtech Arena.
Bruma told Hamburger Morgenpost: "Our boss and our general manager have indicated to me that I will be here for a long time to come. They want me to pen a contract for several years.
"I needed to be very patient. I hope that I will be playing now and that I can take the chance.
"I need to play to develop, but of course I am delighted that a club like Hamburg wants to keep me."
Bruma made nine appearances for Chelsea before joining Hamburg on loan in 2011.