Green Bay signed rookie quarterback Graham Harrell from the practice squad Saturday to back up Flynn and placed safety Anthony Smith (ankle) on season-ending injured reserve.
Rodgers hasn't missed a game since he replaced Brett Favre as the Packers' starting quarterback in 2008. Rodgers' health will be evaluated again next week, La Canfora reported.
As of Saturday, Rodgers hadn't progressed through the full protocol of testing that the NFL requires before a player can return to the field after sustaining a head injury. Packers coach Mike McCarthy said earlier in the week that the team would err on the side of caution in determining Rodgers' status for Sunday's game.
Rodgers will wear a new helmet that offers better head protection when he returns to the field.
This time, he couldn't practice all week and was only able to attend meetings Friday.
Rodgers made an appearance in the Packers' locker room Friday. He didn't take questions from reporters, but he appeared alert and upbeat.
Although Rodgers was listed as doubtful, McCarthy said Friday that there was an outside chance the quarterback would be able to play.
"He's working his way through the process," the coach said. "There are stages that you work through. But he's making progress, and I talked to him (Friday). He looks good (and) would like to play."
But Rodgers won't play, leaving Flynn to run Green Bay's offense. The third-year pro out of LSU threw for 177 yards and an interception in relief of Rodgers last Sunday, and wide receiver Donald Driver expressed confidence in Flynn.
"I think we had fun (this week)," Driver said Friday. "It didn't slow anything down. Everything was kept the same. The pace was like going with Aaron. You'd think you would have to nix some things and work some things out, but no. It was just like we don't miss a beat."
McCarthy echoed Driver's sentiments, telling Madison's The Big 1070 that Flynn impressed him with two good days of practice.
The Associated Press contributed to this report.