Pitino said he's encouraged by Ware's rehabilitation from a broken tibia that included a gruesome open wound during the Cardinals' regional final win over Duke on March 31.
The junior was spotted taking jump shots last month and has progressed to riding a stationary bike.
"He's just riding the bike and you can almost see from the X-rays the bone healing," Pitino said. "I'd say, in another month he'll be healed and then he'll start working out a little bit."
Ware's injury became an inspiration for the Cardinals as they finished their Final Four run through Wichita State and Michigan to the NCAA tournament championship. His role as a defensive stopper on a team returning three of five starters should rank the Cardinals high among 2013-14 preseason favorites.