My opinion….OBJ has one last big, multi year contract left him. If he gets it, he will sign. If not - if he needs to “prove it” - he will want to go to a team that offers the best chance for him to offer that proof. That means a team that will offer him the opportunity to do that with a deep playoff run (much like last year).
In a nutshell, if the Rams don’t offer a multi-year deal, he will be signing with someone else, as the Rams, sadly, are not positioned for a deep playoff run.