Cordero, 27, has a 5.75 ERA in 23 appearances across two MLB seasons. He gave up one run in 1 1/3 innings in an outing for the Blue Jays earlier this season, his only appearances in the big leagues in 2019. Cordero has a combined 5.40 ERA across Double-A and Triple-A this season.
Cordero started the season in the Nationals' system before the Blue Jays claimed him off waivers on May 15. The Mariners then claimed him from the Blue Jays on May 27.
In a corresponding move, Chicago transferred left-hander Carlos Rodon on the 60-day injured list. He had Tommy John surgery on May 15.