Bramble has made 34 appearances for the Black Cats since joining in 2010.
Bramble's current contract with Sunderland is set to expire next summer.
"It's still something I'm interested in," Bramble told The Journal.
"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."
Bramble only made eight Premier League appearances for Sunderland last season due to an Achilles injury.
"This season I can just get my head down and focus on football - nothing else, which is the main thing," added Bramble.
"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."