The Italy international is in the final year of his contract and negotiations over a new deal with Napoli have not gone anywhere.
There is an increasing likelihood that Insigne will leave the current Serie A leaders next summer on a free transfer, ending his association with the club.
Everton are keen to talk to Insigne, while Newcastle are claimed to be ready to hand him a lucrative contract.
Inter have also been heavily linked with an interest in Insigne, but according to Italian daily Tuttosport, the Nerazzurri are gradually cooling their need to sign him.
The Nerazzurri want to bring in a new attacker but do not believe Insigne would suit Simone Inzaghi’s system at the San Siro.
The Napoli forward is no longer a player the club are working towards signing him at the moment.
Inter are claimed to have turned their attention towards Sassuolo’s Giacomo Raspadori and he is their preferred target over Insigne.
The Serie A giants are even considering getting the deal over the line to sign the forward in the winter transfer window.
With Inter cooling their interest in Insigne, Everton and Newcastle have one fewer club to battle for Insigne.