Bayern signed Kim, 29, from Napoli in the summer of 2023.
However, the South Korea international has not received regular playing time under Vincent Kompany.
Kim's contract with the German giant extends until the summer of 2028.
Now BILD's Christian Falk reports Chelsea and Tottenham have shown interest in Kim and that he is still on their radar.
Tottenham want another centre-back to seriously compete with Cristian Romero and Micky van de Ven, who are both wanted by bigger clubs.
Chelsea wants to bolster their squad with a centre-back after missing out on Jérémy Jacquet - who is moving to Liverpool this summer.
Kim is happy at Bayern Munich, but a move to Chelsea or Tottenham cannot be ruled out.
