Packers coach Mike McCarthy indicated Monday that he doubted Rodgers would be ready to return this week.
"I would say he's slim to none," McCarthy said.
Although the Packers did not practice Monday, they were required to submit an official injury report that included practice designations because they on Thursday. The Packers said Rodgers would not have participated had they actually practiced.
"Let's be honest -- he's got to practice," McCarthy said. "There's some physical rehab hurdles to get through that he hasn't reached yet. Like I said, it would be a huge stretch for him to play in this game."
McCarthy declined, however, to name a starting quarterback for Thursday's game. He pulled Scott Tolzien in the third quarter of Sunday's 26-26 tie against the Minnesota Vikings and replaced him with Matt Flynn, who rallied the Packers from a 16-point, fourth-quarter deficit.
Flynn said he is going to prepare for the game as if he is the starter.
"I'm going to spend some extra time learning and making sure I have everything down," he said. "All the little nuances -- making sure I have everything down, checks down, everything like that. I'm definitely going prepare like it, but we'll see."
Flynn, the Packers' backup from 2008 to 2011 before he left in free agency, completed 21 of 36 passes for 218 yards with one touchdown and no interceptions. He re-signed with the Packers on Nov. 12.
"Matt played very well; he deserves to start," McCarthy said. "I like the way Scott has grown. So those are the things we're talking about. So we're going to do the best we can to make sure they're both ready."
If Flynn gets the start, he will be the Packers' fourth starting quarterback this season and the third since Rodgers broke his collarbone Nov. 4 against the Chicago Bears.
"We've got to get two quarterbacks ready, frankly," McCarthy said. "This experience that we've gone through the last four weeks with a different quarterback in four straight games, we're taking a hard look at our preparation. Who has the ball at the beginning of the game, we'll let you know down the line. I have no announcements on that yet today."