Mourinho of course had much much more achievements before he started to get worse. Bayern is not the level to drop to like Saudi Arabia or something right away, he will still find some mid level team first at Europe but then I think he will get worse and worse. He has to win the title this season for his entire life to be shaped accordingly.
Even like that I'm not sure Mou will be the first choice in this case. Mou is still one of the coaches who is always discussed even though in terms of performance he has reduced from his prime in the past few seasons. But for Mou and Bayern it will be very difficult because seeing from the scheme that Mou always does and Bayern's philosophy seems to be the opposite for now.
Mou always likes conservative methods by doing an old-fashioned style of play and that is the opposite of what Bayern always do nowadays.
There are other rumors about Klopp for now but these still can't be validated because after all these rumors are growing because of several things such as traffic in particular.
Bayern Munich's leadership should consider and seize the opportunity when Klopp is about to quit his job at Liverpool. Klopp is the most suitable coach for Bayern Munich right now. I support that happening, even though these are just rumors.