I think it will happen. He knows he has a very good thing and a better opportunity in LA (in 2022 and beyond) than pretty much anywhere else.
In the Rams' case, they also were never going to get into the weeds of negotiations with him until the Stafford, Donald and Kupp deals were done. So there is that too.
And frankly, they also might understandably want to see certain medial updates and progress along the way. OBJ is now 4+ months removed from the surgery so they should have a better sense of his progress and timing. Personally I have a hard time believing he plays more than 7 regular season games. I would target the 11/27 game @KC for his return. Get him really healthy and fresh for the stretch run.
So what do you pay a guy that will give you 7 regular season games (and the postseason)? I don't know, but it's not $7M. At least not without some massive incentives- per game bonuses, Super Bowl win/MVP, some "if this in 2022 then that in 2023" triggers, etc.