Alonso was designated for assignment by the White Sox on Thursday, Mark Feinsand of MLB.com reports.
Alonso is slashing just .178/.275/.301 with seven home runs through 67 games this season, prompting the White Sox to cut their losses and remove the lefty from their 40-man roster. The team has not yet announced a corresponding roster move. Given the amount of money Alonso is owed the rest of the season, he has a chance to pass through waivers untouched and opts for free agency.