The prolific forward - who has been recovering from Achilles problems - grew concerned about his first-team opportunities at the Allianz Arena during pre-season following the arrival of new coach Louis van Gaal and strikers Mario Gomez and Ivica Olic.
And it led to him issuing the Bundesliga giants an ultimatum, insisting he will seek a move away during the winter transfer window if he is not used regularly.
Tottenham Hotspur and West Ham were both linked with a move for the front-man earlier this summer, while Roma and AC Milan have also been tipped to take the forward back to his homeland.
However, Bayern chief Rummenigge has now moved to quash talk of the Italian departing Munich.
"In January, none of our strikers will leave," he said on Tuttomercatoweb.
"I have read in the newspapers that we have already sold Toni.
"In fact, we have never had this problem because we are aware of his qualities and we need him.
"Even the coach [Louis van Gaal] is very happy," he concluded.
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Gregg Davies is the Chief Sub Editor of FourFourTwo magazine, joining the team in January 2008 and spending seven years working on the website. He supports non-league behemoths Hereford and commentates on Bulls matches for Radio Hereford FC. His passions include chocolate hobnobs and attempting to shoehorn Ronnie Radford into any office conversation.
