Luck said the allegations center on "activities and roles of graduate assistants, student managers and other non-coaching staff in the football program" in the period 2005-09.
The athletic director said the school had taken steps, such as reducing the number of football graduate assistant positions, to address the issues.
The time period being investigated covers the tenures of Rick Rodriguez, who left West Virginia after the 2008 season, and current coach Bill Stewart.
"I have spoken at length to Coach Bill Stewart and his staff and I am convinced that they believe in operating a fully compliant football program," Luck said. "Coach Stewart and his coaches have my full support, the full support of the Department of Intercollegiate Athletics and the full support of the university."