The former Netherlands international made the comments during an appearance on Bild's Phrasenmäher podcast, where he discussed the situation in Bayern's midfield.
Van der Vaart suggested that Kimmich's long-term position at the heart of the team should not be taken for granted.
“With all due respect, I think Joshua Kimmich's time could come to an end at some point. And you have to be prepared,” he said.
His proposed solution is a familiar face from the Bundesliga, with Van der Vaart naming Barcelona's De Jong as a potential target for the German champions.
“Frenkie's arrival would make Bayern an even better team. He could even play alongside Kimmich at this stage,” he said.
De Jong has yet to make his return to competitive action this season after his injury, adding another layer to the speculation surrounding his future.
The Dutch midfielder has repeatedly been linked with moves away from Barcelona despite renewing his contract, with clubs in both the Premier League and Bundesliga having been mentioned as potential destinations.
A switch to Bayern would also fit a precedent from the past. In 2006, another Dutch midfielder, Mark van Bommel, left Barcelona for Munich.
Van Bommel quickly established himself at Bayern and became an important member of the side, eventually taking on the captaincy.
Van der Vaart's comments therefore put De Jong's name back into the conversation around Bayern's midfield, although there is no indication in the material provided that the German club have made an approach for the Barcelona player.
For now, the suggestion comes from Van der Vaart rather than from a reported transfer negotiation, with De Jong still a Barcelona player and Bayern continuing to have Kimmich as an established option in midfield.