The 6ft 3in Beijing Guoan centre-back,24, is nicknamed 'the monster' and is a rising star in Asia.
Spurs were first interested in Heung-min Son's international team-mate in the close season after Jan Vertonghen left.
Now they are plotting a fresh move as Chelsea could be about to enter the race.
The Stamford Bridge club famously hi-jacked Spurs' move for Willian in August 2013 to snatch the Brazilian from under their noses in a £30million deal.
Tottenham chiefs are anxious to avoid a similar embarrassing and frustrating scenario.
Min-jae's contract expires in December 2021 and his club in the Chinese capital are ready to cash in.