After the 2-2 draw with Hertha Berlin, Rummenigge stated: "No, people. Everyone knows what a cruciate ligament tear means and what downtime is needed."
This weekend, Sane was scheduled to be in Innsbruck to see specialist Dr Christian Fink for his operation.
Fink has close ties to Bayern, but Rummenigge added: "The op has nothing to do with Bayern, we would not presume. He is a Manchester City player. That's a decision from him, possibly in consultation with the medical department of the national team."