Newton suffered two small fractures in his lower back last Tuesday when his truck rolled in a two-vehicle accident near Bank of America Stadium.
The injury is similar to what Dallas quarterback Tony Romo suffered earlier in the season in a Monday night game. Romo missed his next start, then returned the following week with the understanding there would be a certain amount of pain tolerance needed.
Newton did not play in Sunday's 19-17 victory over Tampa Bay. If he can't go against Cleveland, Derek Anderson will start against the team that cut him after the 2009 season.
"The biggest factor will be whether or not they tell me he can protect himself,'' Rivera said. "I don't want to put a guy out there if he can't protect himself. By that, [I mean] being able to run out of the way, scramble out of the way to stay alive, keep the play alive by being able to get out of the way.''
Rivera used the same criteria in deciding to hold Newton out in the opener against Tampa Bay. Newton was recovering from fractured ribs and offseason ankle surgery and wasn't 100 percent in his ability to run and avoid the rush.
Rivera wants to make a decision as soon as possible. He said that probably won't come until he sees how -- or if -- Newton is able to practice Wednesday.
Ideally, Rivera would like Newton to be a part of every practice. That Newton was limited in practice before the opener played a role in him not playing that week.
"Mastering what we do is hard,'' Rivera said. "Two weeks ago, it all came to fruition for us. The Saints game was the high-water mark for him this year.''
Newton completed 21-of-33 pass attempts for 226 yards and three touchdowns in a 41-10 victory at New Orleans. He also ran 12 times for 83 yards and a touchdown as Carolina amassed 497 total yards.
That the Panthers (5-8-1) remain in contention with New Orleans (5-8) and Atlanta (5-9) for the NFC South title will not factor into Rivera's decision on Newton any more than it would have had Carolina been out of the playoff picture.
"What we do is treat it like we do whether we are or aren't,'' Rivera said. "We're not giving anything up, win or lose. We're playing every week as if there's something really important on the line, like there is.
"Believe me, I don't do that.''
The Panthers received good news in that the hyperextended left knee outside linebacker Thomas Davis suffered Sunday was not serious. Rivera said Davis may be limited in practice early in the week, adding that he should be a full go by Friday.
Carolina also reinstated defensive end Frank Alexander, who was suspended for the first 14 games -- two separate suspensions, four and 10 games -- for violating the league's substance abuse policy. The Panthers were granted a roster exemption for Alexander, who Rivera called the most valuable player during training camp.