The South Korea defender's position at Bayern is in focus after the arrival of Jonathan Tah from Bayer Leverkusen last month.
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TMW says Chelsea are interested in Kim, who was outstanding in Napoli's Scudetto triumph two years ago.
A swap deal is set to be proposed, which would see Chelsea offer cash plus Renato Veiga in exchange for Kim.
Veiga spent the second-half of last season on-loan with Juve.