Winkler was designated for assignment by the Cubs on Tuesday, Russell Dorsey of the Chicago Sun-Times reports.
Winkler hasn't looked good this season, struggling to a 5.22 ERA over 47 relief appearances, with his 15.8 percent walk rate standing out as a major concern. His last three outings have been particularly poor, as he's allowed 13 runs while recording just five outs. Michael Hermosillo was added to the active roster in a corresponding move.