The 28-year-old has been linked with a move to Stoke amidst suggestions he will struggle to earn a place in new Black Cats boss Steve Bruce's plans.
Sunderland have already signed Paraguay international centre-back Paulo Da Silva and Bruce is understood to be tracking Manchester City's Richard Dunne.
Nosworthy recognises he will be facing competition for a spot in the first team, but he believes he has the attributes to help his club.
He told the Hartlepool Mail: "People have told me Stoke are interested, but that is the only way I am aware of it. I have not heard anything official - it is just what people say and what you read.
"I am happy to stay here at Sunderland if I possibly can.
Hamstring injuries"I know the manager wants to strengthen his defence and bring in new faces, but I know what I am capable of and I am prepared to fight for my place.
"When there is competition, you have to fight and that is what I am good at.
"It is a real challenge and I am ready to meet that challenge."
Nosworthy struggled with hamstring injuries last season, but he is now happy to be back in pre-season action.
He told: "It has been good to be back in training again.
"The medical staff have put me to the test with endurance running and the hamstring has been fine, which is a relief."