The Chicago Daily Herald says that White Sox GM Kenny Williams has "most likely" inquired about Lance Berkman, but has this quote from Williams:
“I don’t think anyone is really prepared to make any deals right now. And any interest expressed in any players out there who are impact guys has been done so for quite some time. There really isn’t much substance to anything at this stage of the season. Another 30 games, and you’ll start to see talk pick up. But if you’re not playing well it doesn’t make any sense to go down those roads, anyway. You've got to warrant that."
So...noted, I guess.