Spurs have had a summer of upheaval with Kane linked with a move to Manchester City, the appointment of new coach Nuno Espirito Santo and director of football Fabio Paratici.
Sources told ESPN that despite City's interest in Kane, they are willing to wait a year to sign their ideal striker if they cannot prise him away from Spurs. Manchester United and Chelsea have also shown an interest in Kane, who has three years left on his contract.
Son, 29, has formed a lethal partnership with Kane, with the pair scoring a combined 40 goals out of the team's total of 68 in the Premier League last season as they finished seventh.
He joined Spurs from Bayer Leverkusen in 2015 and has gone on to score 107 goals and assist a further 64 in 280 appearances for the club.
The South Korea international also scored the first Premier League goal and first Champions League goal at the Tottenham Hotspur stadium in April 2019.
"It was already a big honour to play here for six years, the club have showed me massive, massive respect and obviously I'm very happy to be here," Son said.
"It's like home, especially with the fans, the players, the staff. There was no decision. It was easy. I'm so happy to be here and will be so glad to see the fans again soon."
Paratici added: "We are pleased to have agreed a new long-term contract with Son as we move towards the start of a new season and a new chapter for the club with Nuno Espirito Santo.
"Everyone can see the real positive impact he has on the club, both on and off the field, and we are delighted that he will play a part in what we are trying to achieve in the coming years."
Tottenham start their 2021-22 league campaign on Aug. 15 with a home game against defending champions City.