Kane, who recovered from a hamstring tendon issue during the three-month COVID-19 shutdown, looked back to his best with two quality goals as Spurs defeated Leicester 3-0 on Sunday.
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The 26-year-old had signed a six-year contract extension in 2018 but told Sky Sports in March he could leave if they do not progress in the right direction.
"I think everyone thinks he's a fantastic player and Tottenham are so lucky to have him because he's the player, the person and the Tottenham boy," Mourinho told reporters.
"All this together makes him really a special player for us that probably would not be so special playing for another team. He's really special for us, he's really special for Tottenham."
Spurs are on course to secure a place in the Europa League next season after Sunday's victory, with Kane scoring his fourth goal in two games.
"We want him to be happy and for him to be happy he wants victories, to score goals, and I'm so happy after an incredibly difficult injury he's coming in the direction where he's going to end the season perfect," Mourinho said.
Tottenham visit Crystal Palace in their final game.