Ware, who suffered a fractured tibia during Louisville's regional final victory over Duke, has been riding a stationary bike and indicated earlier this summer that he hoped to be healthy for the start of practice in October.
But Pitino would not commit to that timetable, emphasizing that the Cardinals plan to "take our time" with Ware's recovery.
"I'm not saying we're going to redshirt him," Pitino told reporters Monday during a news conference to discuss his Hall of Fame induction, according to the Louisville Courier-Journal, "but we'll take our time because it's a very serious injury."
Pitino said he expects Ware to begin his on-court rehabilitation by mid-October. Defending national champion Louisville opens its season Nov. 9 against Charleston.
"He's going to have to get his confidence back," Pitino said. "He asked me the other day if he should look at it on tape for the first time. I said there's no reason to. I never did."
Ware's injury became a rallying point in the Cardinals' run to their third NCAA championship. The 6-foot-2 guard was an important contributor off Louisville's bench as a sophomore last season, averaging 4.5 points in 37 games.
Information from The Associated Press was used in this report.