Davis broke the bone late in the first half of Sunday's NFC Championship Game against Arizona while making a tackle. He did not return.
Carolina coach Rivera said the injury is similar to one former Panthers' wide receiver Steve Smith Sr. played with in 2009.
"My understanding is if everything goes well, it is most certainly something he'll be able to play with," Rivera said of Davis, a team captain. "We're excited about that possibility.
"He's in recovery, doing well. The doctors feel real comfortable about it and we'll see how he is once he gets here tomorrow and the trainers get a chance to look at it."
Davis' wife, Kelly, posted a picture on social media on Monday morning showing her husband wearing a hospital gown and cap.
"I ain't missing the Super Bowl," Davis said. "You better believe that."
Carolina safety Roman Harper suffered an eye injury in the first half against Arizona and did not return. Harper visited the eye doctor on Monday morning. Rivera did not express a concern that Harper would not be ready for the title game.
Fullback Mike Tolbert left in the second half with what officials called a knee injury. Rivera referred to it as a "little discomfort" and added Tolbert was getting the knee looked at by a physician.
Tolbert said after the game the knee was fine.
Rivera said defensive end Jared Allen, who missed Sunday's game with a foot injury, could be ready for the Super Bowl.
"I'm excited for the fact he's got two weeks to get ready and prove to me he's ready to roll, which I believe he will, knowing him," Rivera said. "He probably could have played Sunday."