Insigne, who is now 30, only has a year left on his current deal, and he is reportedly keen on keeping his options open for the summer, looking at what his career will hold in the future.
According to a report from Italian outlet Il Mattino, this has led to the Italian's contract situation to not go unnoticed by several clubs around Europe, particularly Arsenal, who are looking to rebuild their squad this summer after the disappointment of last season.
With the likes of Willian and Emile Smith Rowe being linked with potential moves away from the club, Arsenal need to add to their attacking options ahead of next season.
However, new Napoli manager Luciano Spalletti has claimed that he is keen to hold onto Insigne this summer, despite there being the risk of him becoming a free agent next summer if he opts not to sign a new contract with the Italian club.
"I speak well of Insigne, I spoke to him on the phone (and) congratulated him after a goal scored in the national team," the former AS Roma and Inter coach claimed.
"I told him I would like to take this journey with him by my side."
According to Napoli-based outlet ArenaNapoli, the 30-year-old wants a contract that would earn him £4.3 million per year in order to extend his stay at the Stadio San Paolo.
However, current Napoli owner Aurelio De Laurentiis is not willing to meet those high demands, and hence a move away from the club seems to be likely.
Insigne had an incredible campaign for Napoli, racking up 30 goal involvements in 48 games in all competitions, scoring 19 goals and providing 11 assists.