The 29-year-old played 15 games in his first season in the NFL, passing for 3,385, but the Browns have brought in a new head coach since the end of the 2012 campaign.
Weeden told The Associated Press: "There's going to be changes. Obviously, we've already seen some. But there's going to be competition. The guys that drafted me are no longer there, so I fully expect there to be competition.
"I would want competition. I want to go into camp and compete. If I had won 10 or 11 games last year, that may not be the case, but we weren't able to get that done.
"That's the way professional sports are. Unless you're Tom Brady, Peyton Manning, Drew Brees or these guys, you might as well expect for somebody to try to come take your job. That's part of the business. But it's also the fun part. You get to compete and try to be a winner."
The Browns finished last in the AFC North in 2012.