The Cerezo Osaka winger reportedly turned down an offer from Monaco but has piqued the interest of the Championship side and Scottish Premier League champions
The Cerezo Osaka winger dazzled for his country with two goals and two assists in June's World Cup qualifiers against Qatar and Lebanon, prompting speculation of a European switch.
Several major Korean newspapers have reported that Kim's agency Ivansports has confirmed that Cardiff and Cerezo are discussing a transfer fee for the 22-year-old.
Speaking to reporters at South Korea's Olympic team training on Tuesday at Paju National Football Centre, Kim revealed that he had interest from the Championship outfit as well as SPL champions Celtic.
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"I'd like to play in England or Germany. My agent and officials of Cerezo Osaka are working on my transfer."
Ilgan Sports have also reported that Kim's agency turned down a €6 million [£4.7m] offer from Park Chu-Young's former club, Monaco.
According to the report, Kim declined the offer as he wanted to avoid a Monaco residency visa and military duty issue similar to Park's.