Stafford, who cleared concussion protocol earlier this week, was already ruled out for Sunday's game against the visiting Seattle Seahawks.
He has already missed two of the past three games and he now will have to miss at least three additional games. With the defending Super Bowl champions sitting at 3-8, it would make little sense for Stafford -- who the Rams signed to a four-year, $160-million contract through 2026 -- to return to the lineup for just the final two games of this season.
Stafford sustained a neck injury in Week 11 against the New Orleans Saints after clearing protocol from a previous concussion.