Thompson was designated for assignment by the Brewers on Friday.
The move frees up a spot on the team's 40-man roster for Gio Gonzalez, who was acquired from the Nationals via trade Friday. Thompson has appeared solely for Triple-A Colorado Springs since joining the Brewers, posting a shiny 1.69 ERA across 5.1 innings before being DFA'd. He'll likely report back to the SkySox if he passes through waivers untouched.