The club's CEO expects the 43-year-old to stay at the Allianz Arena for years to come and insists Mario Mandzukic will not be leaving this summer
The former Barcelona boss moved to Bavaria last summer and has promptly delivered the Bundesliga title in record time, as well as progressing to the last four in the Champions League and the final of the DFB-Pokal.
However, he signed just a three-year contract but Rummenigge says the 43-year-old has absorbed the culture of the club quickly and expects his stay in Germany to be a long one.
"I think Pep will be here for longer than many people think because he has absorbed Bayern's culture very quickly," he told Kicker.
Rummenigge also insisted that striker Mario Mandzukic will not be leaving the club, despite the imminent arrival of Robert Lewandowski from Borussia Dortmund.
"I spoke to Mario not long ago and he told me that he wanted to stay. That clears the matter up for me completely."
Bayern face a crunch Champions League clash at the Allianz Arena on Tuesday against Real Madrid, who lead the semi-final tie 1-0 from last week's first leg.