The Jaguars have shown interest in former Ohio State head coach Urban Meyer, who has been putting together a staff and has told people close to him he expects to get the Jacksonville job, Rapoport adds, citing sources.
However, if Meyer decides to stay retired, the Jaguars would then turn their attention to current Buckeyes head coach Ryan Day, according to Rapoport.
Day, Meyer's successor at Ohio State, led the Big 10 powerhouse to the NCAA national championship with a win over Clemson on Friday night.
The 41-year-old will make his first appearance in the title game as a head coach on Jan. 11.
Meyer retired after the 2018 season due to various health issues. His name has been tied to many major college openings in the time since, but Meyer has opted to stay off the sidelines. The Ohio native currently serves as a college football analyst on Fox Sports.
The 56-year-old has won three national championships at the college level - two with the Florida Gators in 2006 and 2008 and one with the Buckeyes in 2014.
Marrone has been the Jaguars' coach since 2016. Despite leading Jacksonville to the AFC Championship game in 2017, the team has gone 12-35 in the three seasons since. The 1-14 Jags have already clinched the worst record in the league and will own the No. 1 pick in April's draft.
Should Meyer - or Day - be hired, he'll presumably have the choice of either Clemson quarterback Trevor Lawrence or Ohio State passer Justin Fields with the first overall selection in the draft. Fields outdueled Lawrence in a 49-28 victory in Friday night's College Football Playoff semifinal. Neither player has declared for the draft.