"A top man on and off the pitch. We negotiated with him in a serious way and fulfilled all his wishes. But it now seems that he wants to do something new for one more time," Rummenigge said Friday, according to Reuters.
Alcantara was linked with a Bayern exit after contract talks reportedly broke down in May as the 29-year-old expressed a desire to seek new challenges.
With one year remaining on Alcantara's current contract, Bayern risk losing the 37-time capped Spain international on a free transfer next summer.
"We do not want to lose any player without any money next year," Rummenigge said of the possibility.
Widely considered one of Europe's elite midfielders, Alcantara joined Bayern for a €25-million fee from Barcelona in 2013. He's featured 230 times in all competitions for Bayern, winning the Bundesliga title in all seven seasons with the club.