Kingsbury was reportedly set to interview with the Arizona Cardinals and New York Jets for their vacant head coaching positions, but USC denied the teams' requests by using an old rule the league has recently started reinforcing.
The NFL reportedly informed team executives at last month's owners meetings that they will now need to request permission from college athletic directors in order to interview college coaches. Failing to do so would be considered "conduct detrimental" and could lead to docked draft picks.
Kingsbury joined the Trojans in December after being fired as Texas Tech's coach following six seasons in charge of the program.
The 39-year-old is viewed as a top offensive mind who has the potential to be the NFL's next Sean McVay or Matt Nagy.