Pochettino was sacked by Spurs in November after five-and-a-half years in charge, six months after guiding the club to the Champions League Final.
The Argentine’s relationship with Levy appeared to fracture towards the end of his tenure, with Pochettino admitting they clashed over transfer policy and at one point telling the club to change his job title because he had no say in recruitment.
Speaking this week, Pochettino admitted to “a lot of friction” at Spurs but revealed he had thanked Levy in a conversation to coincide with the end of his gardening leave on May 19.
“In the last few days, I was talking with Daniel,” Pochettino said. “I wanted to translate my gratitude and that of my coaching staff and all our families because he was the person that trusted us, who gave us the structure to work.
“[Our conversation] was to say thank you for trusting in us. I was a very young coach, with my experience in Spain and my one-and-a-half years in Southampton.
“The football vision at Tottenham was completely different then to what it is now. That’s why it was amazing for us as a coaching staff to go very quickly [to a higher level].
“To be involved and help the club to be the club that it is today is fantastic. Today, Tottenham is one of the best clubs in the world. We feel very proud of that.