McCoy has missed the last two games because of a concussion he suffered on an illegal hit by Pittsburgh linebacker James Harrison on December 8.
The second-year quarterback still hasn't been cleared to practice, but Shurmur answered "nope" when asked Thursday if he has ruled him out for the game.
"He's getting better every day, and again, every injury is different, every rehab is different," said Shurmur. "I'm assuming no (he won't have to worry about the injury long-term) but we'll see when he comes back."
McCoy, who is said to be anxious to get back on the field, would likely be ruled out sometime before Saturday, if at all. Shurmur wasn't sure if McCoy was still suffering from concussion-related headaches.
"He looks fine," the coach said. "I don't ask him every moment how he's feeling so I don't know if that's the case or not."
McCoy has passed for 2,733 yards, 14 touchdowns and 11 interceptions in 13 games this season. Seneca Wallace started the past two games for the Browns, who have lost five in a row to fall to 4-11.
Shurmur said he was expecting Steelers quarterback Ben Roethlisberger, who was sidelined by a high ankle sprain last week, to play on Sunday.
"He's a tough soul so I imagine he's going to want to be out there with his team," said Shurmur.