Sources close to the situation told ESPNChicago.com that Contreras was the one who suggested he be sent to the minors instead of being relegated to the bullpen.
In the meantime, the White Sox have called up left-handed pitcher Jimmy Gobble from Triple-A Charlotte to plug into the bullpen. Left-handed pitcher Clayton Richard will start Tuesday night's game in Cleveland and become the temporary replacement for Contreras.
Contreras had to clear waivers, which meant all 29 teams had 48 hours to claim him and his $8 million-plus contract that remains from his $11 million salary.
In particular, Contreras will work on his split-fingered pitch, which he has not been able to command against left-handed hitters this season.