The website, citing sources, said Alexander underwent revision ACL surgery in January as a follow-up to the primary reconstruction of the knee in August. He was originally injured during a one-on-one drill on Aug. 6, the day before his 25th birthday.
Alexander, set to become an unrestricted free agent on March 11, is unlikely to return to the Chargers next season.
After joining the Chargers midway through the 2012 season, Alexander became a dynamic playmaker for the team, catching 37 passes for 658 yards and seven touchdowns over the final nine games.
Alexander, who played his first two seasons with the St. Louis Rams, has 83 receptions for 1,395 yards and 10 touchdowns in 28 career games.