Being available is only half of it. Someone wanting you is the other half:
Paul Konerko: He’s finally in the last year of that five-year, $60 million contract. He’d still have nearly $5 million coming by late July. And the White Sox should have enough pitching to scramble back into contention. But if not, it’s hard to imagine Konerko would use his no-trade rights to block a deal to a team with a shot to win.