"He was wasting his time," said Mourinho.
"As managers we must have this feeling of what is possible and what is not. When you try to buy Kane it's just an impossible mission."
Mourinho does not expect Kane to be sold and will build his team to suit him, starting at West Ham.
"This is not about me,' he explained. "This is about Mr Levy and the club. He has a vision and part of that is to make the club better and bigger. There is no better and bigger club without a better and bigger team. So, to keep the best players is obviously part of that plan.
"It was not like a promise to me. It was part of his explanation about his vision. Without being specific about players he told me he does not sell players when the manager doesn't want to sell."
Having coached Cristiano Ronaldo, Didier Drogba, Samuel Eto'o and Zlatan Ibrahimovic, Mourinho appreciates the value of an elite striker and sees Kane in this bracket — once he starts to win trophies.
"He's one of the best strikers in the world, no doubt," said Mourinho. "He just needs his team with him, if his team is England or Tottenham, to bring him or to go with him to the next level.
"And what is the next level? Titles. I think he needs to win. He needs to bring something to highlight his quality, the goals he scores, what he brings to the team. He is a top striker and I've worked with some of the top ones."