During his first three and a half years in charge at Spurs, Pochettino has turned them into a top side in the Premier League and led them back to the Champions League, but his work has not gone unnoticed.
However, Levy believes the Argentinian coach would find it more fulfilling to continue his project in North London, rather than move to a bigger club elsewhere in Europe.
In a new book 'Brave New World', which is being serialised by the 'Daily Mail', the Tottenham chairman said: "I would love nothing more than Mauricio still to be our manager in 10 to 15 years' time.
"To really build success you need time, longevity. It's easy to go and become a manager at Real Madrid, for instance.
"It's a fantastic club, don't get me wrong, but winning at Tottenham Hotspur is far greater than winning at Real Madrid — and he agrees.
"Mauricio wants this sense of achievement, this recognition, to be the main guy. And at this club, he can be the main guy.
"At some other clubs, the president is the main guy but that's not how it is here. I'm so low key, I want him to be the main guy.
"Him. Sometimes it's nice to be given something when you are not expecting it, like the Bentley I gave him as a sign of appreciation."