A couple years back, I was attending a course, and the Prof said he was waiting on a decision by his department dean.

The Dean had been hired in with tenure two years earlier, and they were openly seeking another job.

Since they were tenured there is absolutely nothing anyone can do...I don't think I have to tell you the likelihood of announcing the fact you are looking for another position in the private sector and how it would look...and how quickly your current employer would rapidly assist you in your job search requirements...