According to Bruce Levine of ESPN 1000, the White Sox are currently scouting the Padres minor leagues heavily. He reports that the Sox main target is set-up man Scott Linebrink. I can't see the Padres parting with Linebrink while they're in the middle of division race, and their GM expressed the same thoughts.
I have a hard time figuring out how the Sox and Padres would be a fit. You have to figure that they would ask for Josh Fields since they have the worst offensive output in baseball from their third basemen. The Sox wouldn't be scouting the minor leagues if the deal was simply Linebrink for Fields, so I wonder if there isn't a starter involved.