The 52-year-old Spagnuolo was head coach in St. Louis the past three seasons and was fired in January after going 10-38 with the Rams. Before that he was defensive coordinator for the New York Giants, a stint that included a Super Bowl upset of the New England Patriots.
Gregg Williams, who was New Orleans' defensive coordinator the past three seasons, has joined Jeff Fisher's staff in St. Louis.
Spagnuolo and the Saints do not have a contract yet.
Spagnuolo and general manager Billy Devaney were fired Jan. 2, one day after the Rams wrapped up a 2-14 season tied for the NFL's worst.
Before taking over in St. Louis, Spagnuolo had top-10 defenses with the Giants in the 2007 and 2008 seasons. His 2007 defense led the NFL with 53 sacks and the 2008 unit was sixth in the league with 42.
In the Giants' 2008 Super Bowl triumph over New England, their defense sacked Tom Brady five times and held the Patriots, who had led the NFL with an average of 36.8 points per game, to only 14 points.
Before joining the Giants, Spagnuolo was a defensive assistant in Philadelphia from 1999-2006. He coached Pro Bowl players including Brian Dawkins and Lito Sheppard, and helped Philadelphia field a 10th-ranked defense in the 2004 season, when the Eagles made it to the Super Bowl before falling to New England.
Information from ESPN senior NFL analyst Chris Mortensen and The Associated Press contributed to this report.