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."