Gotze’s future has been uncertain since he hinted at a problem with coach Pep Guardiola during the recent Audi Cup tournament in Munich.
Juve have been keeping an eye on the German World Cup winner, earmarking him as a replacement for Arturo Vidal who they sold to Bayern for 35 million euros this summer.
That move is not now likely to happen since Rummenigge says Gotze does not want to leave.
“He’s told the club that he wants to stay here,” Rummenigge said at a press conference in Munich on Thursday, ahead of their first Bundesliga fixture of the season against Hamburg on Friday night.
“If nothing new should arise, then that puts a lid on it.”
Gotze struggled to hold down a regular starting berth last season and it had been rumoured he was having some regrets about moving to Bayern from Borussia Dortmund in 2013.
The chances of him appearing more often this season are no greater, but Rummenigge now expects him to knuckle down and fight for his place.
“At the end of the day, it’s up to Mario, and I’ve told him this,” Rummenigge said. “Of course there’s a lot of competition in his position.”