Ballack worked with Mourinho during the Portuguese coach's first managerial stint with Chelsea.
"Right now Niko Kovac is the head coach and that should be respected," the 42-year-old told Bild.
"He does a good job. [But] one cannot deny that, at some point in the future, the appointment of Mourinho would bring a certain glamour to the club and the Bundesliga.
"It has been seen with Pep Guardiola - his appointment gave the league a giant jolt, even if he did not win the Champions League at the end with Bayern.
"Guardiola introduced a certain style of play, he's an exceptional coach. In addition, the international profile of each club is many times higher when you get Guardiola or Mourinho.
"With a coach like Mourinho, it's probably easier for a club to get top stars. At the moment, the Bundesliga does not have the same appeal for world-class players as the Premier League. But Bayern would be well-advised to have world stars in their team."
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