The White Sox would prefer a right-handed hitting catcher since the lefty-swinging A.J. Pierzynski is their starter, and the Mets are expected to have an excess of catchers once Brian Schneider comes off the disabled list in the next few days. Castro would fit the White Sox better since Schneider is a left-handed hitter. Additionally, Castro is the better hitter of the two.
The Mets found a new catcher in Omir Santos, who's done a nice job since Schneider went on the disabled list -- though, they had been considering a trade for either Castro or Schneider since the winter. Castro's stock seems to have fallen in their eyes, as manager Jerry Manuel delayed a game to pinch-hit Santos for Castro against the Marlins, explaining that Santos had the shorter swing.
Castro makes $2.5 million, but it isn't known how much money the Mets might send to offset that salary.