The Dutch defender has spent the last 18 months in Germany, with the route to first team football at Stamford Bridge currently blocked.
He has also found minutes hard to come by in the Bundesliga of late, but is considered to be an important part of the senior set-up at Hamburg.
For that reason, they are ready to explore the possibility of bringing Bruma - who has a year left to run on his contract at Chelsea - into the club on a full-time basis.
"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."