The 53-year-old Argentinian, now head coach of the United States men's team, was at the Spurs helm for five and a half years before being sacked in November 2019.
He steered the club to four successive top-four finishes in the Premier League and had title challenges in the 2015-16 and 2016-17 seasons, as well as guiding Spurs to the 2019 Champions League final, and would love to have another crack at the role in the future.
"When I left the club I remember one interview I said I would like one day to come back to Tottenham and that is of course ... I am now in the USA I am not going to say no, I'm not going to talk about that," the former Paris St Germain and Chelsea boss said in an interview with Sky Sports.
"What I said still after six or five years, I still feel in my heart that, yes, I would like one day to come back."
Tottenham, now in their second season under Australian Ange Postecoglou, have endured a difficult campaign, exiting both domestic cup competitions in early February and languishing 14th in the league table having collected just 34 points from 29 games.
Their last remaining hope of securing silverware this term comes up in the Europa League, in which they face Eintracht Frankfurt in the quarter-finals next month.
Speaking about Levy, who was the subject of a protest in February as fans vented their frustration, Pochettino said: "Talking about two different sides, professional and personal.
"I've seen always the appreciation in between both, it always was there and is going to be there, the thing to take professional decisions.
"It's true after nearly six years with all that we lived together was tough because I think too many up and downs and emotional things that we lived.
"One thing was professional, another personal and now, like the day after we left Tottenham, we keep always a very good relationship."
