McCoy has missed the last two games with a concussion. His injury has intensified the attention paid to concussions in the NFL.
"He's getting better every day," Shurmur said. "He looks fine. I don't ask him every moment how he's feeling."
McCoy, in his second season with the Browns, suffered the concussion Dec. 8 when he was hit by Pittsburgh linebacker James Harrison, who was suspended for one game as a consequence of the hit.
McCoy went back into the Dec. 8 game, even though team officials later said he had suffered a concussion. The required tests in such cases were not performed on the Cleveland sideline because the team's trainers were not made aware of the severity of the hit.
The NFL has since mandated that a trainer will monitor the game action from the press box to make sure players receive proper attention after hard hits.
McCoy has thrown for 2,733 yards with 14 touchdowns and 11 interceptions in 13 games this season. Cleveland has lost five in a row and will take a 4-11 record into its final game.