The Dutchman has spent a year and a half with the Bundesliga club due to a lack of first-team opportunities at Stamford Bridge.
But even though his recent playing time has also been limited in Germany, he remains in high regard and could see his temporary move made permanent.
"The manager and the general manager have signalled that they would like to see me staying on at Hamburg long-term," Bruma told Hamburger Morgenpost.
"They want me to sign permanently on a long-term contract.
"I feel that I have to play first-team football to progress. I am, however, pleased that a club like Hamburg want to sign a permanent deal with me."
Hamburg general manager Frank Arnesen, who left Chelsea to take the job at the Imtech Arena, added: "We have told Jeff that he is an important player for us and that he will receive regular match action this season."