Gillispie was hospitalized on the same day that Beal said the university is looking into matters stemming from the coach's dealings with his players.
"We are looking into some concerns within the leadership of our men's basketball program," Beal said, reading from a prepared statement. "Student-athlete well-being is something that is our top priority. We take that very seriously at Texas Tech. We are devoting our full resources into looking into this matter."
Beal confirmed that members of the team had met with Texas Tech athletic director Kirby Hocutt but declined to say when the meeting occurred or what issues were discussed. The meeting was first reported by ESPN.com.
Gillispie is entering his second year as coach of the Red Raiders. His first Texas Tech team finished 8-23 and won only one game in the Big 12.
When Gillispie was hired by Texas Tech, he had been out of coaching for two years after being fired at Kentucky after just two seasons. He was named Southeastern Conference Coach of the Year in his first season, but his second team failed to reach the NCAA tournament.
Six months after his firing, Gillispie sought treatment at John Lucas substance-abuse program in Houston. That followed his third arrest for drunken driving in 10 years.
Gillispie got the Kentucky job after leading Texas A&M to three consecutive 20-win seasons. In his previous coaching stop, he oversaw a turnaround at UTEP in which the Miners tied the NCAA record for most improved team from one season to the next.
The Associated Press