The former Chelsea and Porto boss is sought after across Europe and could replace Bayern boss Ottmar Hitzfeld when his contract runs out in June.
Mourinho's spokesman Eliado Parames told the weekly Die Welt: "It's always gratifying when one of the biggest names in football brings up your name. Bayern Munich: why not?"
Bayern's president Franz Beckenbauer added: "Our club needs a big name. He has got to be a great tactician, have already accumulated experience and have command of the German language.
"Mourinho? Why not? He could do a language course between now and the summer."