As a result, the German club is now working on a compensation package for Burnley, where Kompany still has four years on his contract.
Burnley have just been relegated from the Premier League after only one season in the English top flight.
Bayern agreed to part ways with Tuchel in February after falling behind eventual champions Bayer Leverkusen in the title race.
Kompany is the latest candidate in a long list linked to Bayern.
Leverkusen coach Xabi Alonso, Germany boss Julian Nagelsmann and Austria manager Ralf Rangnick all reportedly turned down Bayern’s interest.
Bayern then attempted to hold onto Tuchel, who led them to a Champions League semi-final loss to Real Madrid. Tuchel, however, said the parties “could not reach an agreement” on him staying in the Bavarian capital.
Kompany has Bundesliga experience, having played at Hamburg before joining Manchester City.
He took the reins of Burnley in 2022, taking them to the Premier League as second-division champions a season later.
Kompany however could not keep Burnley in the top division, with the club relegated in 19th place in the 20-team league.
© Agence France-Presse
Photo: Twitter @FabrizioRomano