McCoy, a six-time Pro Bowler, was released Monday by the Tampa Bay Buccaneers after nine seasons. The 31-year-old immediately became one of the top free agents, and it's believed that he would prefer to join a contender.
The Browns have been linked to McCoy throughout the offseason, and a report Wednesday indicated he is intrigued by the idea of playing for the ascending club.
The Colts have the most salary-cap space in the NFL, which could put them in a favorable position if a bidding war breaks out. The Falcons have the least financial flexibility in the league and would have to get creative to add salary.
In 14 games with the Buccaneers last season, McCoy registered 28 tackles and six sacks. He collected 297 tackles and 54.5 sacks in 123 career games with Tampa.