Ware, who does not own a car, was driving a vehicle owned by Matt Case when he was ticketing Oct. 26 for driving 95 mph in a construction zone on Interstate 65 in Barren County, The (Louisville) Courier-Journal reported Monday.
How Ware got the car could be an issue with the NCAA, which prohibits athletes from receiving extra benefits from their status.
Case said he was a long-time friend of Ware and that he loaned the athlete his personal car that evening so he could visit a friend at Western Kentucky University.
He said Ware returned the car to him that night, although the speeding citation was issued about 11 p.m.
"Everybody's making this situation out like I own this car so Kevin Ware can have a car and I'm some big U of L booster," Case said. "I'm 23. I'm paying my own school debt. The situation has been way skewed."
Case said he works full time in sales and engineering and is an organizer of a Louisville event management, marketing and production company.
"It's not like I have six cars and Kevin drives (one of my) cars every day," Case added. "I let him borrow my only car."
Ware missed a scheduled appearance Monday on the ticket in Barren County court. His court date has been rescheduled for next Monday.