Per NFL rule, assistant coaches on teams in the playoffs can only interview while the team is on a bye. Any interview of Shanahan must be conducted prior to the conclusion of the wild-card games this weekend.
The Falcons (11-5) beat the New Orleans Saints 38-32 on Sunday, securing a first-round playoff bye for the NFC South champions. The Falcons will host a second-round divisional playoff game on Jan. 14.
The Jaguars have already interviewed former head coach Tom Coughlin, and also lined up interviews with Arizona Cardinals offensive coordinator Harold Goodwin, New England Patriots offensive coordinator Josh McDaniels and Tampa Bay Buccaneers defensive coordinator Mike Smith, a former head coach with Atlanta for six seasons (2008-14).
Interim coach Doug Marrone is expected to be a candidate for the job as well.
Shanahan is the architect behind the league's top scoring offense at 33.8 points per game for the Falcons.
The Denver Broncos are now looking for a head coach after Gary Kubiak officially stepped down on Monday due to health reasons. Shanahan credited Kubiak for helping elevate his career, serving as Kubiak's offensive coordinator in Houston.
Shanahan's father, Mike, won back-to-back Super Bowls as the head coach of the Broncos with John Elway at quarterback. Elway, now Denver's executive vice president of football operations/general manager, is expected to have Kyle Shanahan on his list of coaching candidates.