Norwood, who did not make a start last season, said that he must prove himself to the new Browns regime at the training camp if he is to be included in the 53-man roster.
"It's a new year," the Miami Herald quotes Norwood as saying. "You need to prove yourself again. You need to do well in the preseason and training camp.
"I'm focusing on doing the right things and catching the football. I'm just focused on being a part of this football team."
Norwood was drafted by the Philadelphia Eagles in 2009 but did not make an appearance before joining the Browns the following season.