Bennett suffered the injury in the first quarter of the Bears' 30-13 loss to the New Orleans Saints Sunday when safety Roman Harper hit the wideout square in the chest with his helmet on a nine-yard completion.
Bennett left the game, and he returned to action for a short time before being ruled out at the start of the second half.
More tests are scheduled, but the outlook for Bennett has improved the past two days.
If, as expected, Bennett is unable to play against Green Bay, it would be a substantial blow to the Bears' offense. Bennett is considered perhaps the most dependable and polished receiver on the roster, and is a preferred target of quarterback Jay Cutler.
The former third-round draft choice is adept at recognizing the blitz and breaking off his route if necessary. Bennett caught 100 passes the past two seasons and has established himself as the Bears' top slot receiver.
Rookie Dane Sanzenbacher saw increased reps in the slot with Bennett out Sunday.
"He's a tough guy to replace," Sanzenbacher said. "He's dependable, the guy has been in the system ... it's going to be a group effort to try and replace him. I think for me, my biggest asset is having him around to ask those questions and get things figured out. So I'll obviously still be in his ear whether he's playing or not, but it's going to take all of us to step up.
"It's an opportunity, anytime a guy goes down you're expected to be able to step in and the offense isn't supposed to miss a beat. They're not supposed to have to change the game plan just because they have different personnel. You get chances at times when you don't always expect to get them, and you just have to make the most of them."
Bears receiver coach Darryl Drake feels Sanzenbacher can handle the assignment with Bennett expected to be on the shelf. The rookie caught three passes for 33 yards and a touchdown versus the Saints.
"I believe in him," Drake said. "He's tough, he's a rookie, he's only going to get better. I don't blink when he's in there. I really, truly don't. That's a good feeling to have."
Jeff Dickerson covers the Bears for ESPNChicago.com and ESPN 1000.