The South Korea defender's position at Bayern is in focus after the arrival of Jonathan Tah from Bayer Leverkusen last month.
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.