Staley joined the Rams this past season and quickly emerged as a solid head coaching candidate. He helped L.A.'s defense finish the campaign as the NFL's best scoring unit just one year after it ranked 17th.
The 38-year-old previously served as the outside linebackers coach for the Chicago Bears (2017-18) and Denver Broncos (2019).
The Chargers fired ex-head coach Anthony Lynn two weeks ago. Lynn posted a 34-32 record - including the playoffs - through four seasons in Los Angeles.
With the arrival of Staley, all eyes are now on the Chargers' offensive coordinator position as the club looks to develop quarterback Justin Herbert. The 2020 sixth overall pick posted a historic rookie campaign after throwing for 4,336 yards and 31 touchdowns.
Retaining current offensive coordinator Shane Steichen is a possibility, according to NFL Network's Mike Garafolo.
Buffalo Bills offensive coordinator Brian Daboll and New York Giants offensive coordinator Jason Garrett also generated interest from the Chargers.