The 22-year-old admitted earlier this week that he was "not satisfied" with his lack of playing time at the Allianz Arena this season.
The defender has only started 10 Bundesliga matches for Bayern this season, and it had been reported that Manchester City were eyeing a summer move for the German international.
Rummenigge, however, has branded Kimmich "our successor to Philipp Lahm" and has insisted that the full-back, who can also play in midfield, will be a key player for Bayern next season.
"We have big plans for him in the future," he told Sky Sports News. "He will be, quite literally, our successor to Philipp Lahm. From next season, he'll get more and more minutes. That's Carlo Ancelotti's plan, at least."
Kimmich, who joined Bayern from RB Leipzig in the summer of 2015, made 36 appearances under Pep Guardiola at the Allianz Arena last season.