Boateng last month admitted he was considering leaving Bayern to once more test himself abroad, having endured a disappointing 2010-11 season at Manchester City.
"His thoughts about leaving Bayern still exist, as his agent has told me," Rummenigge told Sport Bild.
"We know that this topic might be approaching. When a club is interested and Jerome says that he wants to join this club, we will consider it.
"I don't hide the fact that we have a financial threshold, but it won't be low for sure. But I know that Jerome is thinking about leaving."
Boateng has struggled with injuries over the past three seasons and missed the end of Bayern's campaign due to a hamstring issue, but he was still included in Joachim Low's Germany squad for the World Cup.
Low said that Boateng does not appear distracted by his future and is focused on helping Germany defend their title in Russia.
"I haven't heard about that, I didn't read anything and I don't care at all what happens after the tournament," Low said of Boateng's future.
"There have always been situations where players change their team after a tournament. During a tournament there are situations with clubs that create interest around certain players.
"What I can say after the training sessions is that Boateng worked incredibly hard. He worked hard on his fitness levels when he came back on the first day of training, he made an incredibly good impression and also since then."