Kupp, 30, suffered a hamstring injury during training camp. By going on injured reserve, he was mandated to sit out four games.
The Rams (1-2) play the Indianapolis Colts (2-1) on Sunday in Indianapolis.
Kupp is eligible to return for the Oct. 8 game against the Philadelphia Eagles but McVay said this week he would not “pigeonhole” himself to committing to that as the definitive return date.
The Rams have a 21-day window to decide if and when they will activate Kupp to the roster.
”He is practicing next week,” McVay said before Friday’s practice, “and we’re going to see how he feels.”
In 2022, Kupp suffered an ankle injury in the ninth game of the season. The injury required surgery and sidelined him for the last eight games.
Kupp did not participate in voluntary offseason workouts with the team so he could be with his family as they awaited the birth of their third child. He suffered the hamstring injury during a training camp drill, but returned to practice near the end of the preseason and participated in joint workouts with the Denver Broncos.
Kupp, however, experienced another setback, and he traveled to Minnesota to meet with experts.
McVay has said several times that the goal was for Kupp to “return to performance” as opposed to return to play.
“We’re not going to do anything that’s reckless,” McVay said Friday.
McVay said there was risk “walking out this door, getting in your car.” He said Kupp’s feedback on his readiness to return would be paramount.
“If he feels good enough and the situation has been in alignment with we’re ready to get him — we’re going to get Cooper back and ready to compete for us,” McVay said, “because he’s a big part of our team and I know he’s put a lot of work in.”
Rookie Puka Nacua, Tutu Atwell and Van Jefferson have been the starting receivers for an offense that scored only one touchdown in Monday’s 19-16 defeat to the Cincinnati Bengals.