Sanchez created fresh headlines on Saturday when he said he wanted Champions League football.
Arsenal failed to qualify for the Champions League and with 12 months now left on his contract and no agreement over an extension reached, Sanchez's future is in major doubt.
He said: "The truth is that the decision doesn’t depend on me.
"I have made my decision, but now we wait for a response from Arsenal. It depends on them, I have to wait to know what they want."
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Alexis Sanchez's Arsenal future is uncertain
I do not know what he said, we are no longer involved
Bayern have been among the club interested in Sanchez but speaking before they flew to China for pre-season training, where they will face Arsenal in Shanghai, Rummenigge shut down suggested they wanted to sign the Chilean.
Rummenigge said: "I do not know what he said, we are no longer involved."
The Bayern chief then confirmed he had spoken to manager Carlo Ancelotti and the pair agreed no more attacking signings would be made.
He added: "We've agreed with the coach that there will be no more additions in attack. That makes no sense."
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