A return to his native Germany for the 23-year-old winger has been mooted throughout the summer.
He was, however, to suffer knee ligament damage during a Community Shield outing for City against Liverpool.
A long road to recovery is stretching out in front of him, with Sane set to be sidelined for a prolonged period of time.
With that in mind, and with the Bundesliga champions now targeting other options, Bayern CEO Rummenigge has moved to bring the rumours to a close.
He told reporters after a 2-2 draw with Hertha Berlin when asked for an update on the Sane saga: “No, people. Everyone knows what an ACL tear means and what that entails for recovery time.”
Speculation has continued to tick over of late as City have opted to send Sane for treatment at a medical centre in Austria, rather than one in Barcelona preferred by manager Pep Guardiola.
“The player is a player of Manchester City. And if that is what he decided, then that’s his decision, potentially in consultation with the medical division of the [German] national team,” said Rummenigge.
With Sane no longer in their sights, Bayern are looking to tie up a loan agreement for Barcelona playmaker Philippe Coutinho.
Rummenigge said on that deal: “I have a very friendly relationship with the president of Barcelona [Josep Maria Bartomeu]. That was perhaps a little helpful just now.”
He added when seeking to play down talk of Coutinho being a panic signing to appease the demands of supporters: “The name didn’t factor in at all, but rather exclusively his quality.
“Philippe is a player who can raise our offensive potential with his technical quality. He also made a very good impression on us as a person. He wanted to come to FC Bayern. I’ve very happy about that.”
While arrivals are to be expected at the Allianz Arena before the summer window closes on September 2, Rummeinigge is reluctant to be drawn on whether Jerome Boateng could depart.
He said when asked about the World Cup winner’s future: “I cannot say anything conclusive today about that. The transfer market is open until September 2. And then we’ll see how the whole thing develops.”