The Argentinian has been linked with one of their Premier League rivals in recent times.
The Argentinian has been linked with potentially taking over from Louis van Gaal at Manchester United in the summer, but The Sun claims that he is close to signing a brand new deal to stay at White Hart Lane.
And Kane has spoken about how much of a boost it will be if Pochettino does decide to extend his contract at the club.
"He's a great manager and you want the best managers around the world at our club," he told The Sun.
"When you have top managers you want them to stay around for a long time. You can see how the rest of the team has improved under him."
The former Southampton boss has earned a reputation for being one of the most exciting managers in the game currently. The work he did at St Mary's put him on Spurs' radar, and while his first season was unspectacular in the sense that the club finished outside the top four, this year has been sensational for the team.
With six games to go, they are Leicester City's nearest challengers for the title despite Pochettino putting most of his faith in younger players who have no experience fighting near the summit of the top flight.
For example, very few could have imagined the impact that Dele Alli would have had this term, and perhaps even fewer would have predicted that Erik Lamela would have enjoyed a much more promising campaign this time around after a poor start to life in England.
But Pochettino has clearly had no doubts regarding their ability, which arguably exemplifies why it would be such a massive signing for the club if the manager put pen to paper over a new deal.