Kluber (back) tossed a three-inning simulated game Saturday and is scheduled to throw a bullpen session Monday, Paul Hoynes of Cleveland.com reports. Barring any setbacks, he will partake in a rehab game Thursday.

Kluber has been on the shelf since May 3, but it sounds as if everything goes according to plan during his upcoming bullpen session and minor-league rehab appearance then Kluber could be ready to return to the Indians' rotation by the end of May. An update on his condition should become available following his upcoming activities.