McCoy was released by the Tampa Bay Buccaneers on Monday after nine seasons with the team. Cleveland has been linked to McCoy throughout the offseason but waited for his release before exploring an acquisition.
"He's a good player. ... We're going to turn over every rock and let's just see what happens. It's just a visit," Browns general manager John Dorsey said, according to team writer Andrew Gribble.
Several other teams, including the New England Patriots, Indianapolis Colts, New Orleans Saints, Atlanta Falcons, and Cincinnati Bengals, have also reportedly expressed interest in signing McCoy.
McCoy, 31, has amassed at least six sacks in each of the last six seasons.