Mourinho called England captain Kane into his office in his third day in the job after he replaced Mauricio Pochettino in the Spurs hotseat in November last year.
A scene in Amazon Prime Video's upcoming documentary "All or Nothing", which airs on Monday, shows Mourinho sitting down with his star striker, who was a close confidant of the sacked Pochettino, and telling him how they could be good for each other.
"I saw you training yesterday and I have no doubts that you are a leader," said Mourinho. "That is my feeling. The world looks to English football with an incredible respect but they still think that the movie stars of football belong to other places.
"We have to build also your status in that direction. My profile, I am little bit like that as a coach. My dimension is universal and by being with me I think I can help you."
Mourinho told Kane he had better players at his disposal than he had at his former club, Manchester United, saying Spurs had the potential to "explode".
The Amazon documentary begins with Spurs' poor start to the 2019/20 campaign, leading to Pochettino's sacking.
Chairman Daniel Levy, who had a close relationship with the Argentine, said there had been "a lot of heartache" over the decision to sack Pochettino.
Mourinho did not let the cameras affect his management style.
In one of his early speeches to his team he accused them of being too nice, using a string of expletives to urge his players to show some mettle.
And Mourinho revealed that the only advice former Manchester United manager Alex Ferguson gave him when the Portuguese was manager of United was to sign Dele Alli.
Mourinho made the confession to Spurs chairman Daniel Levy in a meeting shown in the documentary.
"Sir Alex Ferguson gave me only one bit of advice in two-and-a-half years: Buy Dele Alli," he said. "'That guy, with that mentality, the way he plays, the aggression he has in mind. This guy is the Manchester United player. Buy Dele Alli'.
"And he (Ferguson) has an eye for a player. But he (Alli) is not a good trainer, we need to find motivation for the guy."
Mourinho was open with his views on Alli in the documentary, often calling the attacker out for his limp efforts in training.
In a one-on-one meeting with the player he questioned whether Alli's "party boy" lifestyle could have contributed to his drop in form.
"There is a huge difference between a player that keeps consistency and a player that has moments," he told Alli. "And that is what makes the difference between a top, top player and a player that has potential."