Pochettino has been confirmed as the new manager at Chelsea following a season where they finished 12th in the league table.
Chelsea are hopeful that the Argentinian will bring big improvements next season and have them challenge for a top-four spot.
Pochettino was also heavily linked with a return to Tottenham as well but he never was a serious option for Spurs chairman Levy.
The Spurs supremo is looking to bring in a young manager who is hungry to prove himself like Pochettino was in 2014 when he first joined the club.
However, Levy does not feel the current 2023 version of the Argentinian is the profile Spurs are looking for.
The Tottenham chairman never contacted the current Chelsea boss about the job despite being in touch since his sacking.
He also did not want to be driven by emotion and bring back the former Spurs boss because of his popularity amongst fans.
Spurs also have reservations over the way things went south for Pochettino in his final year in north London.