Aaron has gone through the protocol of all of the medical testing that’s involved. We would not have put him on the field today if he did not pass that. The conversation I had with Dr. John Gray, we’re going to watch him closely, just like we always do, and I’m sure he’s in the training room right now just to see how he came out of practice. But he felt fine and I communicated with him during the course of the practice. But it’s Thursday. I’ve never made any decisions on injured players coming back on Thursday.
He's passed all his tests so far, but McCarthy hasn't guaranteed he'll play on Sunday either. He did take most of the snaps in practice. From the Journal-Sentinel:
After missing Wednesday's practice due to the concussion he suffered Sunday against Washington, Rodgers took the vast majority of snaps during the part of practice the media is allowed to watch. That's five periods, which all totaled, include about an hour of walk-throughs and individual drills.
This news is probably as good as could be expected. I'm not familiar with the entire concussion protocol, but it sounds like it's going better for Rodgers this week then it went for Bears QB Jay Cutler last week (when he was forced to miss a game).