New Chargers coach Brandon Staley played quarterback in college at Dayton, and Lombardi used to coach the defensive line there.
Lombardi, grandson of Hall of Fame coach Vince Lombardi, spent seven seasons with the Saints before being named offensive coordinator of the Lions in January 2014, but he was fired by Detroit midway through the 2015 season.
If officially hired by the Chargers, Lombardi will join new coach Staley, previously the defensive coordinator of the Los Angeles Rams, and an offense centered around Justin Herbert, the rookie who became the youngest quarterback in NFL history to throw 30 touchdown passes in a single season.
The Saints, meanwhile, will lose another coach on Sean Payton's staff. The Lions hired Dan Campbell, New Orleans' tight ends coach and an assistant to Payton, as their new head coach last week.