The Browns attempted to convince quarterback Rex Grossman to sign with them, but a source said he declined their offer.
Browns rookie quarterback Connor Shaw took the first-team snaps in practice Tuesday and is preparing to start. Thigpen is expected to back him up.
Johnny Manziel is out for the season with a significant hamstring injury and Brian Hoyer is dealing with a shoulder injury.
Thigpen, who was with the Browns during the preseason before being released, has passed for 3,222 career yards, 21 touchdowns, and 18 interceptions for a 72.5 quarterback rating. He also has rushed for 469 yards and three touchdowns.