McCoy has not been medically cleared by team doctors to return to the field after sustaining a concussion from a helmet-to-helmet hit by Steelers linebacker James Harrison 12 days ago. Browns coach Pat Shurmur said McCoy was at the facility Tuesday and took part in team meetings before being sent home again.
Shurmur said McCoy is making progress but isn't likely to be back in time for Saturday's game at Baltimore.
Wallace is taking all the reps in practice.
"At this point, more than likely he'll be the starter, for sure," Shurmur said.
Shurmur did not know if McCoy has visited any specialists on head injuries while he's been out. Browns tight end Benjamin Watson, who had three concussions since July, sought a second opinion last week before the Browns placed him on injured reserve.
Shurmur was vague when asked specifically if McCoy was still experiencing symptoms from Harrison's hit. Shurmur also wouldn't speculate if McCoy, who started Cleveland's first 13 games, will be able to play in the Jan. 1 season finale against Pittsburgh.
McCoy has not spoken to the media since getting hurt. His concussion and the Browns' handling of the injury has prompted the NFL to change to its policies on concussions. After sending medical personnel to Cleveland last week to meet with the Browns, the league will now require teams to place certified athletic trainers in the press box to help monitor head injuries.
League spokesman Greg Aiello confirmed that memos are being sent to all 32 clubs Tuesday or Wednesday to explain the new protocol, which is expected to begin with this week's games. Aiello said the trainer will be able to monitor the entire game without distraction and inform medical personnel on the sideline of any potential head injuries.
Shurmur said he spoke with McCoy "for a long time" and relayed that the second-year QB's "spirits are good."
"Like anybody who wants to play, he's anxious to get out there," Shurmur said. "He understands there's a process he has to go through before he can play again."
The Players Association may file a grievance on McCoy's behalf on the team's handling of his injury.
Smith sustained a "significant" shoulder injury on Sunday against Arizona, but Shurmur says the versatile player will not need surgery. Shurmur says Brown will undergo surgery on his injured knee.
With just two healthy tight ends on its roster, the team signed free-agent tight end Dan Gronkowski and promoted linebacker Brian Smith from the practice squad. Both will likely play Saturday at Baltimore.
Alex Smith finished with 14 catches for 131 yards and one touchdown this season.
Information from The Associated Press was used in this report.