The Italian has seen his stock rise over the past couple of seasons after transforming the Partenopei into one of the best pure footballing teams in Europe.
This season he took them close to the Scudetto but just couldn't quite hold off the challenge from Juventus at the end, and club president Aurelio De Laurentiis has no doubts he wants Sarri to stay on.
The news will come as a blow to Chelsea, who have been considering a possible move for the tactician as they prepare to part ways with Antonio Conte after the FA Cup final.
The former Juventus and Italy boss is set to depart after a turbulent season at Stamford Bridge, where he cut a frustrated figure for the majority of the 2017/18 campaign.
Conte has complained about a lack of squad depth and expressed his dismay about his team's wastefulness in front of goal, and it was a poor defence of the Premier League title as the Blues limped home in fifth place.
With Sarri seemingly out of the running to become their next boss, Chelsea could potentially turn to Luis Enrique, who has been out of work since leaving Barcelona at the end of the 2016/17 season.