Marrone, who opted out of his Bills' contract after guiding Buffalo to a 9-7 regular season record in 2014, worked with new Bears general manager Ryan Pace (2006-08) for three years in New Orleans.
Several sources describe Marrone and Pace as having a "tight" relationship stemming from their time together in New Orleans.
Marrone went 15-17 over two years in Buffalo before deciding to leave at the end of the regular season.
He posted a 25-25 career mark at Syracuse University from 2009-2012, winning a pair of bowl games.
Marrone also coached the New York Jets offensive line (2002-05) for four years before he jumped to New Orleans to serve as the Saints' offensive coordinator.
A first-year NFL coordinator, Austin is a hot name in the coaching carousal thanks to the Lions' defense finishing the year ranked No. 2 overall. The 49-year old is a former secondary coach for the Baltimore Ravens, Arizona Cardinals, and Seattle Seahawks. Austin spent one year at the University of Florida as the Gators' defensive coordinator.
Austin is under consideration in several NFL cities searching for a new head coach, in addition to Chicago. Austin has also been linked to Atlanta, San Francisco and Denver.