The 49-year-old spent 14 years with the German giants where he is regarded as one of their best ever players.
German newspaper Bild are reporting that current president Uli Hoeness is set to step down from the role.
He is expected to announce his decision at the club's next annual general meeting on November 30.
And Kahn, who was capped 86 times by Germany, is reportedly the man to take over.
And it would be far from a coup – Khan and Hoeness are said to be good friends so would get the job with his predecessor's blessing.
Another former Bayern and Germany star, Lothar Matthaus, would not be surprised with the appointment.
He previously said Kahn could even be in the running for the top job – as chief executive role.
Speaking to OneFootball, Matthaus said: "Oliver Kahn should take over the office of chairman of the board from Rummenigge.
"He's a face of FC Bayern, he has Bayern-DNA in him.
"Oliver is an outstanding expert in soccer. He was always ambitious, always educated himself further, including in economic matters.
"I trust him to lead FC Bayern into the future."
Kahn made an impressive 632 appearances for Bayern, winning eight Bundesliga titles as well as the Champions League.
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