The fourth-year back last played in a 24-17 loss to the Raiders on October 16, and has 60 carries for 211 yards and two touchdowns this season.
Browns head coach Pat Shurmur doesn't plan of putting the Arkansas product on injured reserve and believes that he'll return at some point this season.
"Peyton's making progress where we're hopeful that he can be back after next week," Shurmur said.
Shurmur didn't rule out running back Montario Hardesty (calf) for Sunday's game against the Jaguars, but his status is still up in the air.
The Tennessee product has 244 yards rushing on 75 carries, and 12 receptions for 113 yards in seven games played this year.
If Hardesty can't go, Chris Ogbonnaya will make his third consecutive start. Ogbonnaya carried the ball 19 times for 90 yards in Sunday's 13-12 loss to St. Louis.
Wide receiver Mohamed Massaquoi has missed two consecutive games since suffering a concussion on October 23. Shurmur stated that Massaquoi has not felt any post-concussion symptoms "for a couple days."
"We're going to be very careful with that," Shurmur said.
In addition, safety T.J. Ward will miss his second straight contest with a foot injury.