The White Sox designated Brebbia for assignment Tuesday, James Fegan of SoxMachine.com reports.
The veteran right-hander filled a high-leverage role for Chicago this season and recorded two saves and 13 holds, but he hadn't been particularly effective with a 6.29 ERA in 54 outings. Brebbia posted a sub-4.00 ERA in five of his six MLB campaigns entering the season, so he could receive some interest from other teams.