The 25-year-old defender has been a long-term target for Spurs, and according to CNN Turk, they are in talks over finally completing a deal for him.
They allegedly tried to lure him to the club back in 2020, when he was still at Chinese Super League side Beijing Guoan.
After they failed to sign him, the South Korea international then moved to Fenerbahce, where has become a towering defender, being one of the most sought-after centre-backs in European football.
An update from SIC Noticias journalist Pedro Sepulveda recently stated that Spurs have continued to monitor the defender's progress with the Super Lig side, and they also sent scouts out to watch him play against Trabzonspor last week.
Additionally, CNN Turk have claimed that Spurs have entered negotiations with Fenerbahce over securing a deal for the defender at the end of the season.
Apart from this, the report also claims that Spurs face competition for him from the likes of Newcastle United, Chelsea, Arsenal, Juventus and Porto, with Newcastle in particular starting talks, similar to Spurs.
So far this season, Kim has played in 34 games in all competitions, and despite Fenerbahce's struggles, he has been one of their standout stars.
It remains to be seen whether Antonio Conte sees him as necessary enough to sign him in the summer, which seems to be the case given Tottenham's defensive frailties this season.