If they non-tender him, he does become a free agent able to sign anywhere. I think he will be non-tendered but there is no way he will resign with Boston. I also think he will be very surprised how little he will be offered elsewhere.
OTOH, one also wonders how much he actually likes playing baseball. He has had multiple hitting coaches, none of whom have been able to get through to him. JDM changed his whole approach to become what he has been the last few years. Ortiz studied hitting. JBJ has never changed his approach; frankly, I don't really think he actually has a hitting approach other than swing hard and hope it connects.
His D is still very good, but, while I don't see all games, I think it has slipped a little this season. There are others out there who are almost as good defensively, hit more consistently and are cheaper.