The Gunners missed out on luring the 24-year-old Italian international to North London during the summer transfer window, but were understood to be ready to try again in January.
However, Insigne's agent Antonio Ottaiano recently told Radio Marte his client has no desire to leave the Stadio San Paolo.
"Lorenzo's will is to stay at Napoli for life," Antonio Ottaiano told Radio Marte.
"But of course it takes two to share a relationship like that.
"There are no problems, unless the club decides to terminate the relationship. But for now there are no problems."