According to Metro, Gunners boss Arsene Wenger is preparing to make a £17 million bid for the player if he proves his worth in South America.
Despite Insigne's performances in Serie A last season, it seems Wenger is not quite certain of the Italian international's quality, but he is most certainly a consideration for the North London outfit.
Insigne's agent, Antonio Ottaiano, responded to the interest from the Gunners, saying it was very flattering but indicating that his player would likely be staying in Naples, per talkSPORT:
We are honoured that a club like Arsenal could have Lorenzo on their wish list. However, from here to take it to the next level, that is a possible transfer, there is a huge mountain in between named Napoli.
The club consider him without a shadow of a doubt as one of their cardinal players for their ambitious project. Hence, as of today, I don't see that there can be any further developments unless Arsenal speak to Napoli directly and Napoli change their view on Lorenzo's role here.
While hinting that the Naples-born player would likely stay in Serie A, Ottaiano is not completely ruling out the Arsenal move.
But Wenger himself is right to seek further proof of Insigne's worth before trying to snap him up, as it is not certain that he is what Arsenal need.
They certainly need greater attacking talent and depth at the Emirates, as the Gunners faded from table-toppers to fourth place in the Premier League last season.
Olivier Giroud was often isolated leading the line, and Arsenal need to bring in support for the French striker. They also need to add goals. Only Giroud scored more than 10 for the Gunners in the Premier League last season, per BBC Sport.
This is where the issue lies with Insigne. There is no doubt he is a talented attacker, as proved by his standing in the Napoli team and his World Cup call-up for Italy.
However, his scoring record is not fantastic by any stretch of the imagination. He netted only three times in 36 games as Napoli finished third under Rafael Benitez last season and just five times in 37 games the season before, per Squawka.
In the 2011-12 season, while on loan at Pescara, he scored 18 goals as he combined to great effect with Ciro Immobile and Marco Verratti, per Tom Rowland of Forza Italian Football. But that was in Serie B.
While he has terrific movement and pace, his lack of goals should be a concern for Wenger, as it is a proven goalscorer that Wenger needs most.
Insigne would provide options, as he can play wide as well as just behind a front man, but what he needs to prove in the World Cup is that he can score goals.
If he finds the net often in Brazil, it may confirm to Wenger that Insigne is the man he wants to inspire his attacking unit and drive Arsenal to a genuine title challenge.
At only 22, Insigne will likely only improve, and he could be a long-term player for Arsenal if he were to make the switch to the Emirates.
However, at £17 million, he may just be too expensive a gamble for a player who will not necessarily bag 20 goals a season, which is what Arsenal need.
Wenger is right to be cautious about an undeniably talented player—not because he is not a quality footballer but because he may not be the player Arsenal need.
If he does not perform well at the World Cup, Arsenal's French boss will likely move to another attacking target who can prove the difference for the Gunners next term.