The Browns invited McGahee to come in for a physical examination on Thursday and intend to sign him if his medical checks out.
There is no certainty, however, that McGahee will pass the test. The player saw his 2012 season with the Denver Broncos end prematurely following a leg injury.
Chris Ogbonnaya and Bobby Rainey are the current running backs on Cleveland's roster. If McGahee is signed he is expected to have a prominent role during the team's 2014 season.