Updated: Sep 8
It is believed Bayern have spoken about a potential move for Sane.
The COVID-19 pandemic has caused serious uncertainty across the globe.
Leroy Sane transfer news is becoming a hot top like last summer.
The German winger Sane was a transfer target for Bayern last summer, and reports continue to link the 24-year-old with a move to the Allianz Arena.
Speaking to SportBild, Rummenigge said the Bavarians won’t be signing any player for a large fee when the transfer window opens as the COVID-19 pandemic has given a blow to the football world.
"I'm not talking about players who are under contract to other clubs," Rummenigge said.
"I can only talk about the value of our players. One thing is clear: We too must act with foresight under the new circumstances.
"It is the task of Hasan Salihamidzic, Oliver Kahn and the coach to think about the squad planning for next season. That includes possible entries, but also exits.
"[Large fees] depends on the individual case. There will still be players who demand a high price. But the big question is: Who is able to pay this price?
"Cash is a position that no longer exists on a large scale in professional football. Maybe it's good that we are becoming a bit more rational and stable. After all, the risk for clubs has been increasing in recent years."