Perryman, who suffered the injury in Sunday's preseason game against the Seahawks, will undergo an MRI on Monday, the source told Schefter.
Perryman hobbled off the field Sunday after injuring his left ankle in the first quarter. He was taken to the locker room on a cart and returned to the sideline using crutches and wearing a walking boot.
A long-term injury to Perryman would be another significant blow to the Chargers, who have been hit with multiple injuries this preseason.
Perryman, 24, was slated to be Los Angeles' starting middle linebacker after recording 72 tackles, two sacks and an interception in 12 games -- 11 starts -- last year.
The Chargers already are without rookie receiver Mike Williams, who will miss training camp while recovering from a lower back disk herniation. Coach Anthony Lynn said last week that Williams, the Chargers' first-round draft pick, has resumed running and is making progress.
Los Angeles also will be without the services of rookie guard Forrest Lamp, the team's second-round pick, who has a torn ACL in his right knee.
ESPN's Eric D. Williams and The Associated Press contributed to this report.