Manchester City supremo Pep Guardiola has thrown his weight behind the Belgian.
Kompany, who was relegated with Burnley in the Premier League this season, is now at the very top of the sport in Germany.
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"I'm happy the link has happened for Bayern to Vinny," Guardiola said last week.
"I have a huge opinion about Vinny, doesn't matter the relegation with Burnley.
What I felt playing against him and knowing him, I have the highest opinion of his work, personality, his knowledge of the game, how he handles the media.
"I'd love Bayern to take the best decision. I love that club. I'm in love with Bayern Munich for many many reasons.
Hopefully take the best decision, if they believe Vinny is the right decision, for Munich they will have a guy to support unconditionally."