Kansas City hasn't finished higher than 24th in yards allowed per game since 2016 and ranked 24th in scoring defense in 2018.
Among the potential replacements, Schefter noted former New York Jets and Buffalo Bills head coach Rex Ryan was "a name to watch" after he received offers to become a defensive coordinator in recent seasons.
Spagnuolo previously worked with Reid from 1999 to 2006 as defensive assistant, defensive backs coach and linebackers coach. He also spent three years as head coach of the St. Louis Rams, going 10-38 from 2009 to 2011.
The 59-year-old most recently served as defensive coordinator for the New York Giants from 2015 to 2017. He also took over as their interim head coach for the final four games in 2017 after Ben McAdoo's firing.