Speaking with BBC Sport, Pochettino made the admission when discussing the departure of Tottenham chairman Daniel Levy.
He said, "I was very surprised. We still keep in touch. Our relationship was always good. His legacy is there. It's amazing what he did for the club.
"We're in contact and one day I'd like to share a coffee with him. He made it a possibility for me to manage a club like Tottenham - one of the best clubs in the world with an amazing fanbase. I'm very grateful to him and proud to be part of the family of Tottenham.
"Talking about the Premier League, and we are in London... to win the Premier League and the Champions League. We were so close in Tottenham. I want to achieve this.
"I am still young, I have the energy, experience and motivation to try in the future. Outside, to make my family feel proud - my sons, my wife, my dog, my horses, my mum and dad, my granddaughter..."