McCaffrey, who suffered an oblique/rib injury in Sunday's loss to the Cleveland Browns, underwent an MRI on Monday.
San Francisco left tackle Trent Williams (right ankle) and wide receiver Deebo Samuel (shoulder) also have a chance to play in Monday's game, sources said. The 49ers will make a determination on who can and can't play over the course of the next week.
Samuel was forced to leave Sunday's game late in the first quarter because of his shoulder injury, while Williams gritted through his ankle sprain.
McCaffrey left the game in the third quarter but returned for one play -- a 6-yard run with just under three minutes left in the quarter -- before heading to the sideline and then the locker room. He was officially ruled out early in the fourth quarter.
ESPN's Nick Wagoner contributed to this report.