The Royals optioned Klein to Triple-A Omaha on Friday.
Klein was added to the Royals' 40-man roster in November after posting a 5.66 ERA and 1.85 WHIP across 35 innings in Triple-A last season. He struck out six batters over 3.2 scoreless frames during spring training, but he will need to prove he can find consistent success in the minors before getting the call to join Kansas City's bullpen.