The 22-year-old was a regular under Pep Guardiola at the Allianz Arena last season but has found his opportunities in the first team far more limited since Carlo Ancelotti took charge.
Speculation has mounted that Guardiola could look to bring him to the Etihad Stadium for next season, with the City boss eager to bolster his options in defence, but Rummenigge insists that Kimmich has already been earmarked as a successor to retiring captain Philipp Lahm.
"We have big plans for him in the future," he told Sky Sport. "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 also operates as a midfielder, has made 30 appearances this season, scoring seven goals.