The Chicago Tribune reported early Friday that Cutler suffered a mild MCL sprain, and ESPNChicago.com confirmed it was a mild knee sprain.
The Bears officially listed Cutler as probable for Sunday's game against the Green Bay Packers.
"What knee? Believe me, I know there is a guy that reported that there is a problem with the knee, but there is no problem with the knee," Smith said. "Jay is good to go. We are hoping he'll play the best game he's ever been able to play."
Cutler was knocked out of Sunday's loss to the Minnesota Vikings with a neck injury. He has maintained all week that he'll be ready to go Sunday against the Packers.
"It's a lot of things at this point," Cutler said with a laugh on Monday, when asked on "The Jay Cutler Show" on ESPN 1000 what part of his body hurts the most. "I don't know if I'm getting old or what's happening, but it's getting harder and harder."
Smith said Thursday that he doesn't expect Cutler to suffer any loss of mobility.
"No, none at all," Smith said Thursday. "He practiced today without any trouble at all. After a hard-fought game like that on the turf, you sometimes have some bumps that last a little bit longer. He should be fine."
"We're a little banged up, but believe me, we have enough guys to play this week," Smith said.
Bears defensive tackle Henry Melton (chest) and defensive end Shea McClellin (knee) are both listed as doubtful. Neither practiced on Friday, although Smith did say Melton was back at the facility after being excused Thursday for personal reasons.
The Bears re-signed veteran defensive tackle Amobi Okoye on Wednesday to provide depth at the position in the event they would be minus Melton on Sunday.
ESPNChicago.com reported on Thursday that Bennett would miss his second straight game due to the concussion he suffered on Dec. 2 in an overtime loss to the Seattle Seahawks. The receiver has not been cleared by the team's medical staff to resume football related activities.
"He hasn't been cleared, and we haven't had one (a concussion) that has gone this long," Smith said. "Of course it is a concern when you have missed this much time, but hopefully he will eventually be OK."
Running back Michael Bush returned to practice despite sitting out Thursday. Bush reinjured his ribs last weekend and played only two snaps in the Bears' 21-14 loss to the Vikings.
Hayes' knee injury prevented him from finishing the game last weekend. If Hayes is limited or unable to play Sunday, the Bears are expected to turn to special teams ace Blake Costanzo to fill in at linebacker.
ESPNChicago.com's Michael C. Wright and Jeff Dickerson contributed to this report.