I know they have rules against tampering, that's why coaches like Marvin Lewis and Romeo Crennel got fucked over for head coaching jobs for so long, because they weren't allowed to be interviewed during the playoffs, so teams would hire other coaches before Lewis and Crennel were allowed to interview.
I don't know if this applies for the regular season or if they even interviewed Johnson, but I know that up until last year, assistant coaches of teams in the playoffs weren't allowed to interview for other head coaching jobs in the NFL. College is a different story.
I know they can FIRE their current coach. But someone already on the staff would have to take over.