Reports have linked the Gunners with a £20 million bid for the 23-year-old, while his representative had previously claimed that Insigne was “honoured” by links with the Premier League club.
Yet Fabio Andreotti has now said that there has been no contact between the two clubs over a transfer, with Napoli in no mood to sell the Italy international.
"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, who was a part of the Italy squad that were eliminated at the group stage of the 2014 World Cup, scored nine goals in all competitions last season.