While no determination has been made on Rodgers' status, a source told ESPN the Packers doubt the quarterback -- who revealed Tuesday that he suffered pain in his injured left collarbone while making simple movements on the practice field last week -- will be cleared to play.
A scan performed last week showed that Rodgers' collarbone had not fully healed. He still must be medically cleared for game contact.
Rodgers was listed as a limited participant in practice Wednesday, but he took part in more of the practice than he did last week. In fact, tight end Andrew Quarless said Rodgers took some snaps with the starting offense during team periods.
"Oh man, 12 looked real good today," Quarless said after practice. "It was good to see him out there really working with the offense. He was out there before but wasn't working as much with the offense. But today he took some offensive reps, which is a great thing for the team, definitely."
The key will be how Rodgers feels Thursday. Last week, the soreness he experienced after his first day of practice forced him to curtail his work. Rodgers was not available for comment Wednesday but is scheduled to speak Thursday.
"I didn't think he was in pain today from what I saw," coach Mike McCarthy said. "But that's really a question for him."
McCarthy said team doctors still have not cleared Rodgers for game action.
"I think it's important to stay in tune with that," he said. "The topic of 'Is he playing the game?' versus 'Is he medically cleared?' are two totally different issues. Aaron's obviously very important to our organization. He's the face of our franchise and until he's medically cleared, just like any other player going through a significant injury, that's where the focus will be."
Some medical experts believe it is unlikely Rodgers will be cleared because he is less than six weeks removed from suffering the injury. A source told ESPN that complete bone formation typically requires eight to 10 weeks, meaning Rodgers would be taking a risk by playing before at least eight weeks of healing.
The Packers' medical staff is considered around the league to be conservative in returning players to the field prematurely from injury. Until sufficient bone healing has taken place, Rodgers is at risk for a non-displaced fracture that would require surgery and interfere with his offseason.
Rodgers talked about his recovery Tuesday on his ESPN 540 Milwaukee radio show, acknowledging that he experienced more pain than he expected when he returned to practice last week.
"We would need different results and different responses to be able to get on the field this week," he said.
Rodgers said he was able to throw the ball without discomfort but that things changed once he moved around during full-speed drill work. Tasks such as taking snaps and handing off with his left arm were painful.
"I shouldn't be having pain doing some of the simple movements," Rodgers said.
The Packers (6-6-1) are preparing Matt Flynn to start against the Cowboys (7-6), who rank last in the league in defense.
Flynn kept Green Bay in the playoff hunt this past weekend with the team's first win since Rodgers was injured Nov. 4 against the Chicago Bears. With three games remaining, the Packers trail the NFC North-leading Bears (7-6) and Detroit Lions (7-6) by a half-game.
ESPN.com Packers reporter Rob Demovsky contributed to this report.