The 24-year-old is entering the final year of his rookie deal signed in 2010 after being selected by the club in the first round of the NFL Draft.
Despite their lack of success on the field, Haden is keen to remain in Cleveland.
He told NFL Network: "That's what we're working on now. I've been [in] the league four years and been putting my blood sweat and tears out there. We haven't been successful. There's been a lot of regime changes.
"We do have talks as far as moving forward, 'What's going to happen?' You don't have that long in the league to play your best ball, so put your best foot forward.
"We definitely have those talks and that definitely comes into consideration. You want to win. Money is good, but when you tell people you play for the Browns and they chuckle it hits home because you go out there every day and grind and work and the owners and new coaching staff knows that."
Haden recorded 54 tackles and four interceptions in the 2013 season.