Bramble, who made his first Premier League start of the season in last weekend's 1-1 draw against Liverpool, will be out of contract at the Wearside club next summer.
The central defender, 31, is determined to become a first-choice pick for Martin O'Neill this season and convince the Black Cats boss to offer him a new deal.
"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, 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. "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."