Rummenigge explained that contract talks between Thiago and Bayern sporting director Hasan Salihamidzic have broken down as the Spanish midfielder wants to move.
The chairman of the Bundesliga champions told Sky Germany: "The talks Hasan (Salihamidzic) had with him have always been very productive. And at some point it actually seemed that [a new contract] was done.
"But then Thiago told Hasan some time ago that he would like to try something new at the end of his career. We have to accept that."
Thiago has a year left on his current contract and Rummenigge insists that the player - who has been linked with a transfer to Liverpool - will leave on the club's terms.
He explained: "We have a contract with Thiago that is still valid for one year and if he reaches an agreement with any club then that club should pay a transfer fee of a certain amount.
"No club has contacted us to date and wants to have concrete discussions with us.
"We will only start negotiating for his sale from a certain amount. There will be no summer sales at FC Bayern.''
Rummenigge added that there was no ill-feeling between Thiago and the German club.
He said: "I'm not angry at all, I like him. I think he's a great footballer, a fine footballer and he's a good character too.
"And one shouldn't forget either: At 29, he is at an age where, if he wants to do something new, he has to do it now because if you are in your 30s, it will be more difficult to make transfers."