Mbappe rejected the chance to join both Real Madrid and Liverpool this summer after signing a new blockbuster three-year contract to remain at the Parc des Princes.
With this new deal, the 23-year-old forward is believed to have been granted more control with regards to how the club operates, including the position of the manager.
According to L'Equipe, Mbappe has a 'great relationship' with Pochettino and has told the club's hierarchy that he would the happy to work under the 50-year-old again next season.
Pochettino's future in the French capital has been speculated for several months, with a switch to Manchester United mooted before they opted to appoint Erik ten Hag.
Sporting Lisbon boss Ruben Amorim is believed to be the favourite to replace Pochettino should the latter, who has less than 18 months remaining on his contract, leave PSG.