Kane said last weekend he was happy at Spurs but added his boyhood team needs to continue to make progress and start winning titles.
With 30 goals already in all competitions this season, Kane has established himself among the very best players in the world.
But Pochettino, who has admitted Kane could never be forced to stay, believes the 24-year-old would prefer success at Tottenham over any other team.
"Harry is happy. Always, I told our fans, he is happy," Pochettino said.
"He loves Tottenham and only that everyone wants to win - us, the club, (chairman) Daniel Levy, the players, the fans - everyone wants to win, and wants to win in the place you love.
"For Harry it's so special to win titles and trophies at Tottenham.
"Of course, at the moment he achieves a lot of individual awards but he would like to offer our fans and the club collective trophies."