Alleva had been criticized recently for his handling of men's basketball coach Will Wade, who was suspended before the NCAA Tournament for not cooperating during an investigation into possible recruiting violations. Wade was reinstated after the tournament.
The veteran director previously came under fire for the way he managed the football program, too. In 2015, he was set to fire coach Les Miles but changed his mind at seemingly the last moment. He then fired Miles the next year and struggled to land a high-profile replacement.
Alleva celebrated his 11-year anniversary at LSU on April 4. He came to the Tigers by way of Duke.