Shams Charania of The Athletic and Stadium first reported the possibility of a torn ACL.
Wojnarowski reported Cousins left the court while working out after "'bumping knees' with another player."
Injuries have become a recurring problem for the four-time All-Star over the past two seasons. He ruptured his Achilles in January 2018 while playing for the New Orleans Pelicans, causing him to miss the rest of that season.
After he signed with the Golden State Warriors in July 2018, Cousins missed the first 45 games last season rehabbing his Achilles. The 29-year-old also sat out 14 playoff contests due to a quad injury he suffered in Game 2 of their series against the Los Angeles Clippers.
In 30 games with the Warriors, Cousins averaged 16.3 points and 8.2 rebounds.
The Lakers took a chance on Cousins by giving him a one-year deal worth $3.5 million. He was joining LeBron James and reuniting with Anthony Davis—after they played parts of two seasons together in New Orleans—with the goal to win a title in L.A. in 2019-20.
If Cousins is on the shelf for an extended period, Lakers head coach Frank Vogel can use Davis as his primary center with Kyle Kuzma at power forward. JaVale McGee is also available if they want to keep Davis at the 4.