The program reportedly hopes to finalize a deal with the former NFL coach soon.
Marrone was fired in January after six seasons in Jacksonville, the last four as head coach. He led the Jaguars to the AFC Championship Game in 2017 but couldn't post more than six wins in a season in the years following. The 56-year-old also coached the Buffalo Bills from 2013-14, compiling a 15-17 record.
If he takes the Alabama job, Marrone will return to the collegiate level where he coached Syracuse from 2009-12. He helped lead the Orange to two eight-win seasons and left the program with a 25-25 record.
The hire would also reunite Marrone with former Houston Texans coach Bill O'Brien, who's expected to be named Alabama's new offensive coordinator. Both men worked together on Georgia Tech's coaching staff in the late 1990s.