Pochettino’s five-and-a-half-year stint in charge of the Lilywhites was cut short last month following a difficult start to the season.
The former Espanyol and Southampton manager established Tottenham as regular top four finishers during his time at the club and led them to their first ever UEFA Champions League final in June, where they lost out to Liverpool.
Pochettino left Tottenham in 14th place on the Premier League table, but his successor, Jose Mourinho, has steadied the ship with four wins in five league games to them up to fifth, three points behind fourth-placed Chelsea, whom they meet on Sunday.
Levy admits his relationship with Pochettino made it incredibly difficult to get rid of him, but has tipped the Argentine to make a return sometime in the future.
"You have to understand I had built up a personal relationship with Mauricio over five and a half years," Levy told the Evening Standard.
"It is not something I ever wanted. Personally, it was incredibly difficult, I told him that and he understood.
"He's been in football [a long time], he understands. It's not personal and I'm sure he'll come back stronger and get an opportunity to manage another great club. Maybe one day he'll come back to us.
"I'm not going to sit here and analyse the past. It's not productive. Mauricio did a fantastic job for us, we are very grateful. I wish him all the best for the future.
"I'm still in contact with him. My relationship is very good with him. It just got to the point where it felt we needed a divorce."
