Well, they could keep him around. As for "signing him to a one year deal," his service time going into this season was 3.077 years - he'll be a second-year arbitration-eligible player this winter. Is he worth a second-year arbitration award? He'll be 30 in November. His offensive numbers are... well, offensive. His minor league numbers...not particularly encouraging. But yeah, they could keep him - I don't know in what role, though; based on his history, he's not likely to oust Brandon Marsh, and I don't see him on the roster ahead of Hall, Vierling, Maton. He's not as productive as any of them (in a bench role), and he's older than any of them.
Moreover, if somebody more attractive hits the waiver wire tomorrow morning, Zimmer could be DFA'ed by tomorrow afternoon.