PSG have sacked managers in the past after falling short in the Champions League, but sources have told ESPN the club is happy with Luis Enrique's work and believe he can take the club further.
The Spanish coach, who turned 54 years old on Wednesday, signed a two-year deal when he joined PSG last summer and could begin talks over an extension soon.
Luis Enrique has been a favourite among fans this season, including the club's hard-core supporters who chant his name at every game.
The task of guiding PSG to their first Champions League title will become much tougher next season should Kylian Mbappé go through with his decision to leave the club at the end of his contract this summer and join Real Madrid.
However, Luis Enrique has not shied away from star-player exits at PSG -- he made the bold decision to allow Neymar and Marco Veratti to leave the Parc des Princes last summer -- and has instead focused on instilling a team spirit and identity at the club.
Despite their Champions League run having come to an end, PSG could yet add to their trophy haul this season in the French Cup final on May 25 where they face Lyon.
PSG have already lifted Ligue 1 this season in Luis Enrique's first season in charge, as well as the French Super Cup.