His contract had been set to expire in 2021, and Bayern may now be forced into scrambling for a potential buyer this summer rather than allowing him to slip away on a free transfer a year later.
Liverpool are being linked with Thiago and Rummenigge told BILD: "He's a great guy on and off the pitch. We negotiated with him and met all of his wishes.
"But Thiago Alcantara wants to leave. It looks like he may want to do something new at the end of his career.
"We don't want to lose a player for free next year. I say that very clearly."
Rummenigge has denied being contacted by Liverpool.
He added: "We haven't had any contact with Liverpool."