The central defender, 31, will be out of contract at the Wearside club next summer.
Bramble, who joined Sunderland from Wigan in 2010, only made eight top-flight appearances last season after missing almost five months of the season with an Achilles injury.
Titus Bramble: "It's still something I'm interested in.
"If I'm playing games I don't see why I won't get offered a new contract. Of course I want to stay.
"I'm very happy up here and I would love to stay.
"This season I can just get my head down and focus on football - nothing else, which is the main thing.
"The challenge for me is to play as many games as possible because we've got four or five centre-halves and four of them are over 30."