McCullers (forearm) threw 25 pitches in a bullpen session Tuesday, Brian McTaggart of MLB.com reports.
McCullers reportedly reached 91.6 mph with his fastball during the bullpen session. The next step will be for the right-hander to mix in some breaking balls in his next session, which will likely take place before Saturday's game against the White Sox in Chicago. McCullers will then need to rebuild his arm strength and likely go on a lengthy rehab assignment, but the latest positive developments give him a chance to join the rotation in the early part of June.