Burdi, 22, has a 5.24 ERA and 33:12 K:BB in 22.1 relief innings for Triple-A Charlotte.
The 6-foot-3 righty has converted five of seven save opportunities, but he's been battered recently, allowing nine earned runs in his last four appearances. With David Robertson firmly entrenched as the White Sox closer and the big club sitting in last place, there does not appear to be a reason to rush Burdi to the show, although he could get a look after the trade deadline if Robertson and/or Nate Jones are sent elsewhere.