The Arizona Cardinals are starting McCoy after Kyler Murray was ruled out with a hamstring injury that he suffered last week.
"He's improved," one Cardinals source said of Murray, who had been listed as questionable. "But [he] needs to be able to open up and run before the game to get the green light."
The Rams had been preparing as if they will start Wolford, even as Stafford has shown signs of improvement from his concussion symptoms throughout the week, according to sources.
Stafford was placed in the concussion protocol on Tuesday, and he had been listed as questionable against the Cardinals. Rams coach Sean McVay said Friday that Stafford is "making good progress and steady progression."
Wolford will be backed up by Bryce Perkins, a 2020 undrafted free agent whom the Rams think highly of.
Los Angeles will see the return of running back Kyren Williams, who was activated off injured reserve Saturday and will play Sunday. Williams will be used with Darrell Henderson Jr. and Cam Akers to help upgrade the Rams' rushing attack.
McCoy, 36, started three games last season when Murray was sidelined because of an ankle injury, leading Arizona to a 2-1 record in those contests. McCoy has started 33 games over his 13-year NFL career.
Wolford, 27, appeared in three games with the Rams last season, but he has not started since L.A.'s 2020 regular-season finale and its wild-card playoff victory over the Seattle Seahawks.