BILD says Bayern are willing to sell the South Korea international this month for the right offer, with the aim of financing the arrival of another centre-back.
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Chelsea are interested, having Kim on their shortlist as they seek an experienced centre-back signing before the winter transfer window closes.
Along with Kim, Manchester United defender Harry Maguire has also been discussed at Stamford Bridge.
At Bayern, Kim - who arrived from Napoli - has a deal at Bayern to 2028.