The centre-back, who is currently on the books at Chinese Super League side Beijing Guoan, is a team-mate of Spurs star Heung-Min Son at international level for South Korea.
Kim has caught the eye with his assured performances both in Chinese football and on the international stage and Tottenham had him firmly on their radar last summer.
No deal was done for Kim however and the defender stayed in China with Beijing Guoan.
However, with the Chinese season now over, Spurs are continuing talks with Beijing Guoan for Kim, according to Italian broadcaster Sportitalia.
It is unclear if Tottenham will try to bring in Kim during this month’s transfer window or seek to put a deal in place for the summer, but Bejing Guoan’s 2021 season would be in full swing by that point.
The centre-back has been capped by South Korea on 30 occasions so far and has made a total of 57 appearances for Beijing Guoan.
He could be tempted by the prospect of a move to the Premier League to link up with Son.