The Bundesliga club believes Kompany wants to join them, and the two clubs want to agree on a compensation price.
Kompany, 38, is expected to go to Munich alongside his Clarets backroom team, which includes former Wales international Craig Bellamy.
Bayern have struggled to find a replacement for Thomas Tuchel, whose departure was confirmed last week following an original announcement in February.
Bayer Leverkusen manager Xabi Alonso, Germany’s Julian Nagelsmann, and current Austria coach Ralf Rangnick have all declined the position.
Talks about convincing Tuchel to stay failed to yield a favorable result, leaving Bayern with a predicament.
