Kupp was injured in the first half of the Rams' 23-20 win over the Denver Broncos on Oct. 14.
"Cooper's making good progress," McVay said. "Whether it's this week or whether it's another week, hard to say right now. We're just taking it a day at a time with him. But, very positive in terms of just the way that he's responding to some of the rehab. And we'll whether that means he's a go for this week or not."
Kupp has 30 receptions for 438 yards and five touchdowns this season. The 25-year-old also has four carries for 25 yards.
Josh Reynolds received the majority of snaps in Kupp's place and finished with one catch for 19 yards in Sunday's 39-10 win over the San Francisco 49ers.
"I thought Josh Reynolds did an excellent job stepping up," McVay said. "And then Nick Williams comes in and makes two big catches. The one third down where Jared (Goff) works through a progression and gets to him, makes a nice tight catch in traffic. And then he made a catch on a second down that got us into a third-and-manageable. So he came in and did a nice job understanding what his role would be. How that affects the way that we go into this week is really going to still be predicated on our gameplan, once we get a little more into the Green Bay film and things like that."
The undefeated Rams (7-0) will host the Green Bay Packers (3-2-1) on Sunday (4:25 p.m. ET).