The North London outfit were thought to be considering a £20m offer for the 23-year-old, who is said to have felt flattered by reports linking him to the Emirates.
However, the player's agent Fabio Andreotti has insisted that Napoli are not looking to sell the forward in this summer window.
"We have not been contacted by Arsenal for Lorenzo Insigne and Napoli has not notified us of this interest," Andreotti told Italian radio station Radio Crc.
"Lorenzo is a target of several European sides so it wouldn't surprise me if big clubs are interested in him. However, Napoli don't want to put him in the market."
Insigne scored nine goals for Rafael Benitez's side in all competitions last season.