Rapoport added that the two sides "have mutual interest" but that "nothing is done."
Faulk, a seven-time Pro Bowler and three-time All-Pro who won the Associated Press' 2000 NFL MVP award, is one of the most decorated offensive players in football history.
The former San Diego State star played from 1994 to 2005 with the Indianapolis Colts and St. Louis Rams, winning two NFC titles and one Super Bowl.
Faulk worked as an NFL Network analyst in his post-playing career from 2015 to 2017.
In December 2017, former NFL Network wardrobe stylist Jami Cantor sued the network and said that she was "subjected to ongoing and continuing sexual harassment by current and former on-air talent," per TMZ Sports. That talent included Faulk, who was suspended as the result of the investigation and did not return to work for the network. NFL Network reached a settlement with Cantor, and the case was dropped.
Faulk would not be the first ex-NFL star to become a head coach at a historically Black college or university should he reach an agreement with Southern. Pro Football Hall of Famer and former defensive back/returner Deion Sanders now leads the Jackson State program. JSU went 4-3 under Sanders this year.
Southern is in the market for a new head coach after Dawson Odums resigned to take the Norfolk State job on April 20. His successor has big shoes to fill, as Odums went 63-35 overall and 53-17 in the SWAC, including the 2013 SWAC Football Championship.
Last year's Southern team went 5-1, including a win over Grambling State in the 47th annual Bayou Classic.