The Metro reports that Arsene Wenger will study the player during the World Cup and then make a possible £17 million bid to bring Insigne to the Premier League.
The 23-year-old Italian international has had a consistent season in Serie A this year and would add strength to Wenger's attack.
Insigne has featured 46 times for Napoli in the past year in domestic league and European competition, per WhoScored.com.
Arsenal centre-back Laurent Koscielny has publicly stated how important it is that Wenger recruits striking talent during the transfer window, per Peter Edwards of the Express:
Yes, we need to recruit a very, very good striker, because it's important for us, for competition for places, because Olivier [Giroud] needs that to become even better.
Having a striker who scores more than 30 goals a season can help us win the Premier League. Compared to the squads like Manchester City, even United, Chelsea. ... You can see there's a certain difference
However, Insigne is not the type of striker Koscielny is hoping for. The Italian only hit the net on six occasions last season, per WhoScored.com. He plays more in the channels than centrally.
AS Roma Press editor John Solano recently highlighted Insigne's lack of goals when compared to Italy's other top attackers who missed out on being picked for the World Cup finals.
Olivier Giroud needs the competition in the striking position to remain on his toes and give the Gunners the goals they need.
Insigne will not offer this even though he is a talented individual in his own right.
If Wenger does move for the Napoli player, there is always the option of moving Theo Walcott into the centre and finally allowing him to become a centre-forward.
Walcott has matured greatly in recent times and his eye for goal is as sharp as any striker plying their trade in England.
This move would allow Alex Oxlade-Chamberlain to play in a more wide attacking role and free up Walcott to move from the right-hand side of the attack.
Despite his injuries last year, Walcott hit five goals in 13 Premier League games, per Squawka. A move to the striker's role would see this ratio improve. He may just be the player Wenger needs to win more trophies—the only question is whether the manager has faith in him to deliver the goods.