Clarke (oblique) threw a live session Tuesday and felt good afterward, Anne Rogers of MLB.com reports.
Clarke will throw again Friday, and if all goes as planned, he will spend a little time on a minor-league rehab assignment before returning to Kansas City ahead of season's end. The 29-year-old reliever was in the middle of a career year, having posted a 4.02 ERA and 1.19 WHIP before being sidelined in early August with an oblique strain.