I'm pretty sure it doesn't matter, AFU, I think it's based on the manager leaving his job, whether sacked, resigned, whatever.
From
Bet365
"Bets struck are on the next permanent manager to leave his club. If no manager has left his position by the end of the last scheduled league fixture, then the 'No Manager To Leave' option, will be deemed the market winner."
Souness now 4/6 favourite, by the way