Cleavinger (forearm) recently tossed a bullpen session, Eric Stephen of SBNation.com reports.
Cleavinger hasn't pitched since May 15 and hit the injured list May 18 with left forearm irritation. He is currently rehabbing at the team's training facility in Arizona. The left-hander is expected to go on a rehab assignment of at least one week when he is ready to pitch in games.