The club could not be immediately reached for a comment.
Heynckes was brought in on the basis that he would steady the ship until the end of the season after Carlo Ancelotti's sacking.
They had also been beaten 3-0 at Paris St Germain in the Champions League.
Currently, the ideal coach for FC Bayern, "said Club CEO Karl-Heinz Rummenigge".
"I would not have returned to any other club in the world", he told Bayern's official website.More news: 16 people killed after train collides with bus
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In an interview with Kicker magazine, Heynckes said he was "not making a comeback, it's a service for a friend".
Very special means our togetherness with Jupp, "said Hermann who admitted heavily leaving Fortuna who is now leading the Bundesliga standings 2, a caste under the Bundesliga".
Two German coaches believed to be in the running to manage Bayern - Nagelsmann and former Dortmund manager Thomas Tuchel - have no previous experience with the Bavarian giants. I decided on this because owe a lot to Bayern.
Celtic travel to face Bayern on October 18, before the Bundesliga champions visit Glasgow a fortnight later.
"He's a great professional and a great person".
He made 39 global appearances, scoring 19 goals for West Germany.
Heynckes retired from football after winning the club's only treble in 2013 and will take charge of the team together with his assistants Peter Hermann and Herman Gerland.