Indians pitching coach Mickey Callaway and head athletic trainer James Quinlan heard good reports from Kluber's throwing session on Saturday.
"Mick told me he felt good," Indians manager Terry Francona said. "He was OK to continue. Mickey and James and myself, we're going to get everybody on the same page about when he's going to pitch because he'll most likely go to a Minor League game, and then we'll go from there. But we want to talk to him and make sure that everything is all right."
Kluber, who landed on the 10-day disabled list on May 3, was at Progressive Field on Sunday stretching.
In 37 1/3 innings this season, Kluber is 3-2 with a 5.06 ERA over six starts. The 2014 American League Cy Young Award winner has 41 strikeouts and 13 walks, but he has surrendered seven home runs.
Richard Dean is a contributor to MLB.com based in Houston. This story was not subject to the approval of Major League Baseball or its clubs.