Spurs are stepping up their pursuit of a new manager now that the season is over, with a list of high-level candidates under consideration.
Antonio Conte has been linked after the former Chelsea manager left his post at Inter Milan in the wake of leading them to the Italian title.
Erik Ten Hag, Graham Potter and Ralph Rangnick are also admired.
But the potential return of Pochettino would be the most intriguing option – and a way for Levy to smooth some of the tensions with supporters over his involvement in the failed European Super League plans.
Whether their former manager will be allowed to leave PSG, where he is under contract until next year, will be the major sticking point.
But Levy was always open to the possibility of bringing Pochettino back, despite sacking him just five months after he led the club to the Champions League Final.
In an exclusive interview with Standard Sport in 2019, the Spurs chairman said: “You have to understand I had built up a personal relationship with Mauricio over five-and-a-half years. It is not something I ever wanted. Personally, it was incredibly difficult, I told him that and he understood.
“He’s been in football, 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.”
Spurs’ move for a new manager will gather pace now that the season has been concluded.
They were keen to avoid disruption to other clubs in the final weeks of the campaign out of respect to other clubs, with their primary targets already believed to be in jobs.
With the season over Spurs are now free to make the necessary approaches to the names on their list.
Pochettino would be seen as a returning hero to Spurs fans – and maybe even provide some hope that he could convince Harry Kane to put aside his plans to leave this summer.
Alternatively, any money received from Kane’s proposed transfer would go a long way to helping the 49-year-old rebuild the squad he left behind.
Pochettino has won his first trophies as a manager with PSG – guiding them to the French Super Cup and the Coupe de France. But he failed to win the title, which PSG have won seven times in the previous eight seasons.
He also failed to end their search for a first Champions League crown – being knocked out by Manchester City in the semi-final.