The Spain international has cemented his status as one of the top midfielders in Europe during his time with Bayern, and has been a fixture in Hansi Flick's side in 2019-20.
Thiago's performances in the middle of the park helped Bayern secure yet another domestic double, with the prospect of a first treble since 2012-13 also on the cards when the Champions League resumes next month.
However, the 29-year-old only has one year left to run on his current contract at the Allianz, and Flick has admitted that the playmaker has ambitions to "experience another big league" before he calls time on his career.
Liverpool has been mooted as a potential landing spot for Thiago, and Jurgen Klopp fuelled speculation over his future by expressing his admiration towards the ex-Barca star earlier this month.
Rummenigge says the Spanish star has made Bayern sporting director Hasan Salihamidzic aware of his desire to undertake a new challenge away from the Bundesliga, but insists that the club hasn't been contacted by Liverpool or any other potential suitors over his availability.
The Bayern CEO told a press conference on Thursday: "Hasan had talks with Thiago. They were always very positive, but he told Hasan some time ago that he wants to do something new to finish his career.
"So far no club has contacted us. We don't know if he's settled things with a new club. Hasan is in talks with David and his advisor.
"So far we haven't found a solution. We want to extend. If that's not possible, we have to look."
Manchester City boss Pep Guardiola has been among those to weigh in on Thiago's situation at Bayern, having worked with him at Barcelona between 2008 and 2012.
When asked if the midfielder would be able to adapt to the demands of English football, the former Blaugrana manager told reporters: "A player who plays for Barcelona and Bayern Munich can play in the Premier League. Of course he can play. He’s an exceptional player, but I don’t know what he’s going to do.”