McCarthy did say Monday that the team wants to make a decision on Rodgers' availability "sooner than later."
Rodgers, who has not played since fracturing his left collarbone against the Bears at Lambeau Field on Nov. 4, has missed the past seven games.
Including the loss to the Bears when Rodgers was injured at the end of the Packers' opening series, the Packers have gone 2-5-1 with three different starters at quarterback.
Throughout the process, the team has emphasized that Rodgers has not been "medically cleared" by team physician Dr. Pat McKenzie.
McCarthy also emphasized last week that the decision not to start Rodgers in Sunday's 38-31 loss to the Pittsburgh Steelers was an "organizational decision," suggesting that general manager Ted Thompson, McCarthy and McKenzie made the call.
"(There is) lot of conversation going on with Aaron and obviously Dr. McKenzie and Ted Thompson and I. We're working through that," McCarthy said Monday of the team's plans for Rodgers.
"I do not have anything to announce today. Hopefully we can get the question answered sooner than later. We're still working that."
Asked directly if Rodgers has been medically cleared, McCarthy's answer was different than previous answers to the same question.
"That's all part of the conversation. We're still gathering information today," McCarthy said. "There's testing and things to get done, so we're still working through that. I, personally, haven't talked to Dr. McKenzie yet. He left for surgery. We're working through it."
Last week, McCarthy had also said that Rodgers looked "ready to play" after observing him in practice last Wednesday and Thursday.
While Rodgers had experienced pain in his shoulder after returning to practice in advance of the Dec. 8 game against Atlanta, he was essentially pain-free before the Dec. 15 game against Dallas and before Sunday's game against the Steelers.
"Clearly after seeing Aaron practice for two weeks, this is something Ted Thompson and I need to sit down and we need to assess all the information and to decide if it's time for him to play," McCarthy said.
"Aaron wants to play, has wanted to play for the last couple of weeks. He fully accepts, understands everything going on with his injury, so this is really a decision for Ted Thompson and I representing the organization. That's how it works."
Backup Matt Flynn had led Green Bay to back-to-back double-digit comebacks in victories over Atlanta and Dallas the previous two weeks to keep the Packers' playoff hopes alive.
And their loss to Pittsburgh ended up having no ill effect because of the Bears' 54-11 blowout loss at Philadelphia later in the night.
Now, the Packers (7-7-1) and Bears (8-7) will square off Sunday, with the winner earning the NFC North crown and a home playoff game in the NFC wild-card round.
"We know what's at stake," Flynn said.
Rodgers' status isn't the only issue for the Packers on the injury front. Four-time Pro Bowl outside linebacker Clay Matthews, who missed four games earlier this season after breaking his right thumb against Detroit on Oct. 6, broke the thumb again Sunday and may be lost for the season.
"The training staff didn't feel very good about the injury, so we're still working through the process," McCarthy said.
And running back Eddie Lacy, who has been hobbled by a sprained right ankle since suffering the initial injury Dec. 8, hurt the ankle again Sunday and could be out, too.
"Eddie, he's sore, which he has been pretty much the whole season," McCarthy said. "We're not going to practice on the field until Thursday, so I'll probably have a better feel for where he's at."
The Packers have 16 players on injured reserve, including wide receiver Randall Cobb, who has been designated for return but has yet to be medically cleared for game action.
Defensive end Johnny Jolly was the latest starter to be placed on season-ending IR on Saturday with a neck injury.
And yet, here they are, with a chance to win the division.
"It's been a wild ride so far. And I like to think we're just getting started," McCarthy said. "That's what I'm selling. Hopefully they're buying it."