The 29-year-old former Barcelona midfielder has been linked with a number of clubs, including a switch to the Premier League champions
The 29-year-old, formerly of Barcelona, has been linked with a move to Liverpool in recent weeks, with his contract at Bayern set to expire next summer.
Rummenigge confirmed Bayern have been in contract talks with Thiago, but he seemed to suggest that the discussions have so far come to nothing.
“He is a top boy on and off the pitch,” Rummenigge told Bild.
“We had serious negotiations with him and fulfilled all of his wishes. But it looks like he might want to do something new again at the end of his career.
“We have never had any contact with Liverpool. If he wants to do that, we have to deal with it.
“We don’t want to lose a player for free next year. I say that very clearly.”
Rummenigge expanded on the situation in an interview with Sport1, also commenting on the future of David Alaba.
Like Thiago, Alaba is out of contract next year and he has been linked with a number of clubs – including a reunion with Pep Guardiola at Manchester City.
“Everything seemed fixed [with Thiago],” Rummenigge added.
“Hasan [Salihamidzic, sporting director] has had discussions with his advisor. We had the impression that all the conditions were okay so far. Now he is obviously dealing with doing something new again. Let’s just wait and see.
“Both are top guys, on and off the pitch. We now have to try to find a solution that is financially acceptable to us. We know that both players have a contract for one year.”
Bayern completed the signing of Leroy Sane on Friday from Manchester City, but Rummenigge confirmed that Kai Havertz of Bayer Leverkusen wouldn’t be following him.
“I’ll be very clear: Financially speaking, we won’t be able to transfer Havertz this year,” he said.
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“All of European football, Bayern included, are currently facing major financial challenges for as long as it is not possible to play in front of spectators again.
“It’s a decision that Bayer Leverkusen and the player have to make [whether he leaves].
“To be honest, I would also like for Havertz to stay in Leverkusen for at least another year, because we want to have competition.”