The two-time AL Cy Young Award winner could begin a minor league rehabilitation assignment Thursday as he continues to make progress in his recovery after being struck by a line drive hit by Miami's Brian Anderson on May 1.
Kluber began playing catch about six weeks ago. He's been throwing in the bullpen for a couple of weeks and will have another side session Tuesday.
"Now that I'm getting to face hitters, hopefully that comes with getting to pitch in a game sometime soon," he said. "It's not a finished product by any means right now, but I'm looking forward to it."
Kluber threw 35 pitches to hitters from Akron, the Indians' Double-A team, in a session at Progressive Field. He hit 88-89 mph and threw several breaking pitches.
"I just thought he looked healthy, and that's good," manager Terry Francona said. "Now he has time to perfect his craft, which he's really good at. We need to give him that time."
Kluber, who went 2-3 with a 5.80 ERA in seven starts before the injury, has been trying to proceed on a step-by-step process.
"I don't have a reference point to compare it to," he said. "I'm not trying to look at it as a big picture, but for my sanity, try to break it into smaller pieces of the puzzle."
Cleveland's rotation depth has been tested this season. Carlos Carrasco was diagnosed with leukemia in June and Mike Clevinger missed two months with a back injury before returning to win his past five decisions.