The Dutch defender has spent the last 18 months in Germany and has a year left to run on his contract with the Blues.
"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 added: "We have told Jeff that he is an important player for us and that he will receive regular match action this season."