His success (20 strikeouts, two earned runs in his last 12 innings) since returning from the disabled list may accelerate a possible deal to improve the Braves' offense. Whether Beachy would be trade bait is anyone's guess, but his emergence could make a veteran such as Derek Lowe available.
The White Sox recently sent Dave Yokum, their fine assistant general manager/pro scout, to watch Beachy and Braves' pitching, so we'll see if there's any match, and whether the White Sox would ever consider dealing Carlos Quentin.
Cafardo is usually reasonable and smart whenever he speculates at a potential trade, but this rumor just doesn't make sense.
For one, the last thing the White Sox need is another starting pitcher. They currently have five solid starters in Edwin Jackson, Philip Humber, Gavin Floyd, Mark Buehrle and John Danks, and that doesn't include Jake Peavy, who is currently recovering on the disabled list. While it's always nice to add depth, the White Sox don't have any pressing need or void to fill.
Secondly, the Braves haven't even hinted at moving Beachy and, in my opinion, he's the pitcher least likely to be traded outside of Tommy Hanson or Julio Teheran. He's young, cheap, under contract for another five or six seasons, and a very promising starting pitcher. I would believe the speculation a little more if the scout was in attendance to watch Jurrjens, Lowe or one of our Minor League pitchers, but not Beachy.
Finally, I'm not so sure the White Sox have anyone the Braves would be interested in acquiring. Cafardo mentions Carlos Quentin, but he's a) injury prone, b) a terrible defender and c) a free-swinging slugger with bad plate discipline. The Braves aren't looking to add all of that to their club in exchange for a few home runs.
Take the rumor for what it's worth. I'd assume it's pretty safe to rule out any potential deal between Chicago and Atlanta, though I guess you should never say never.