Source: A.J. Pierzynski files as FA
The White Sox have exclusive negotiating rights with their free agents through Friday.
The team is not expected to pick up Peavy's $22 million option, which would mean it would pay a $4 million buyout. That doesn't mean he won't return to Chicago, but general manager Rick Hahn has talked about how desirable Peavy would be to other teams on the free-agent market.
Pierzynski, 36, is coming off a career season in which he had 27 home runs and 77 RBIs.