The Burnley manager is set to be named Bayern coach this week, though many on the board had wanted to see Hansi Flick return.
"There was - let's say - discontent in the last few days. The top bosses, including Uli Hoeness, once again supported Hansi Flick," reports Sky Deutschland's Florian Plettenberg.
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The former Bayern coach, who won the sextuple with the record champions, is now close to signing a contract with FC Barcelona.
Sporting director Max Eberl is said to have prevailed on this point and pushed through the appointment of Kompany. It's unclear whether Hoenes was convinced with arguments or simply outvoted.