Earlier this season, Cumpton started two games for the Pirates. He allowed six runs in 12 2/3 innings.
"He's fresh and he's shown up well," manager Clint Hurdle said. "I think we have seen a lot of velocity. The fastball velocity might be a mile or two faster."
Hurdle also said closer Jason Grilli would have his next simulated bullpen sessions on Tuesday and Wednesday. Grilli is recovering from a strained left oblique.
Nate Taylor is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.