McVay's announcement came a day after Stafford was placed on injured reserve. Although he is eligible to return from IR in Week 17, McVay said "there's a good chance" the quarterback will not play again this season.
Stafford has been sidelined since he injured his neck in the Rams' Week 11 loss to the New Orleans Saints, a game he left after being evaluated for a concussion. McVay later said Stafford felt some numbness in his legs after taking a hit in that game.
Stafford cleared the concussion protocol on Friday but was held out of Sunday's game.
Stafford was playing against the Saints just two days after he was initially cleared from the concussion protocol. He first entered it Nov. 8.
In nine games this season, Stafford has completed 68% off his passes for 2,087 yards with 10 touchdowns and eight interceptions.
Rams backup quarterback John Wolford started Sunday against Seattle, completing 14 of 26 passes for 178 yards and two interceptions.