The 2012 first-round pick (22nd overall) has played in 23 game the past two seasons, throwing for 23 touchdowns and 26 interceptions with a combined passer rating of 71.8.
It's possible Weeden was going to be cut regardless of what he wanted as it might be difficult to land a draft pick in a trade for a 30-year-old quarterback.
Weeden wanting to start fresh would be no surprise. He had become a lightning rod for fan frustration in his two seasons with the Browns.
The Browns are expected to draft a quarterback with one of their high picks, and Brian Hoyer, who tore his ACL in Week 5, is expected to be back in time for training camp after flashing some potential in the two games he played last season.
Cleveland is in the midst of a major overhaul of its front office as Ray Farmer is replacing Mike Lombardi as general manager, CEO Joe Banner is transitioning out of the organization and Mike Pettine was recently hired as head coach.
The NFL Network reported the news on Weeden earlier Wednesday.