Sarri's future is the subject of speculation amid reports he could take the head coach role at Juventus, vacated at the end of 2018-19 by Massimiliano Allegri.
But Insigne urged his former boss to remember that he guided Napoli to three consecutive top-three finishes in Serie A during his time at the helm and in doing so etched his name into the club's history.
"It's speculation that gives me displeasure," Insigne told a news conference ahead of Italy's Euro 2020 qualifier against Greece.
"He did so much for us players and all the Neapolitan people. He's also a professional, but him choosing Juve would hurt.
"It will be a betrayal for us Neapolitans once it becomes official."
Insigne, 28, has represented Napoli for his whole career and played some of his best football under Sarri.
The Italy international indicated Sarri's legacy at Napoli could be affected by a switch to the Bianconeri, saying: "I'm sorry to think about him sitting on the Juventus bench.
"He was very important to me for many reasons. I hope he changes his mind. If he went to Juventus he would hurt us but I can't blame him. It’s his decision."
Jorginho, who played under Sarri at Napoli and then followed him to Chelsea, recently said it would be "sad" if the 60-year-old manager was to leave Stamford Bridge after just one season.