What is the value to signing him before the post season finishes?
If he has a good post season, he will not have earned more than he's already asking for. And if another team backs up the truck for him, and he wants to accept that over a very, very reasonable (most likely overly reasonable) offer from us...then he doesn't really want to be here and we use that open 11-13 million to spread around multiple holes.
If he has a very poor post season then we can much better assess what we really want to do.
I just don't see any value to signing him prior to the post season. None.