Mourinho is regarded as one of Europe's top coaches, having recently added to his ever-growing list of achievements by guiding Real Madrid to the Liga title this season.
Despite speculation surrounding his future at Real, Mourinho has confirmed he is committed to the club ahead of the 2012-13 season.
Regardless, Schweinsteiger has talked up the possibility of the Portuguese one day taking the reins at the Allianz Arena, should they go searching for a successor to Jupp Heynckes.
"I have to admit that I see Mourinho as an excellent coach. Unfortunately he doesn't speak German. Either way, I believe Mourinho is a coach who would definitely be successful with Bayern," Schweinsteiger told Bild.
"I would very much like it if Bayern think of Mourinho if we are ever in the market for a new coach."
Mourinho, though, recently told Sport Bild: "I'd love [to work in Germany] but to be fair, it's very important in my skills as a coach to know the language.
"To communicate with the players, to be with the press in a very comfortable way because the media are a very important part of our job and I'd think I wouldn't be at the top of my potential working in Germany, so it's out of my mind.
"But because of the quality of the game and of many things I understand in German football, yes I would like it."
Bayern met Real in this season's Champions League and ultimately booked a place in the final against Chelsea as they won on penalties after the aggregate scoreline finsihed 3-3.