Rodgers is officially listed as questionable with a shoulder injury. Rodgers did some throwing on Friday, and McCarthy reported he is making progress.
Matt Flynn handled the snaps Friday with the first team, and McCarthy said he could go either way on Sunday with the decision. He's going to give Rodgers a chance to throw on Sunday morning to see where he is.
"Hopefully [Rodgers] will feel good tomorrow," McCarthy said, according to the Milwaukee Journal Sentinel. "He feels good. His rehab has been positive."
"The strength is improving," McCarthy said, according to the report. "How he responds tomorrow will probably tell the tale. ... I'm preparing to go either way."
Listed as doubtful are running backs Korey Hall (knee) and Kregg Lumpkin (hamstring) and cornerback Jason Hunter (hamstring). Despite missing practice with his broken toe, cornerback Charles Woodson is probable and will start.
Linebacker A.J. Hawk is questionable with a groin injury and will be a game-time decision. McCarthy said Hawk is still very sore because of the injury. Defensive tackle Ryan Pickett is probable with a knee injury and will play.
John Clayton is a senior NFL writer for ESPN.com.