Metro reports that the Azzurri forward could be available for the relatively humble price of £10 million, with the player said to be keen on a Naples exit.
It would be an ideal piece of business for the Gunners to round off their attacking makeover this summer, with Wenger still lacking that star depth in quality up front.
As things stand, Olivier Giroud is still likely to hold down his place as the team's totem in attack, but the addition of Alexis Sanchez has given Wenger a new malleability to work with, an end to which Vargas' acquisition would only help even more.
The manager is eager to show that Arsenal are ready to compete with their fellow powerhouse peers once again, per The Independent:
We are less vulnerable now, that is for sure. In the last two years we bought Ozil and Sanchez - five years ago we would have lost Ozil and Sanchez.
We have more money available to buy today than we had five years ago. We can compete better. For years we have lost top players without the ability to replace them because of financial management.
For some, Vargas is far from the most impressive prospect. A World Cup (or any other major international tournament) has a habit of glamourising players in the short term who have otherwise been lacklustre on the club scene.
The 24-year-old has guilty of such crimes in recent years, spending time on loan at Valencia and Gremio since signing for Napoli, failing to impress current boss Rafa Benitez.
However, Vargas also has a tendency to showcase the sublime, and if his genius can be stretched into more consistent terms, he can indeed be a force in his own right.
OptaJose displays what a potent part of Jorge Sampaoli's attack the player was during Chile's World Cup campaign:
Able to play as a centrepiece of his own alongside a partner or fielded on the flank, Vargas suits the rhythm that Wenger is trying to encourage in north London.
With the likes of Sanchez, a renewed Theo Walcott, Mesut Ozil, Alex-Oxlade Chamberlain, Lukas Podolski and Santi Cazorla in the midst, competition for these places is rife, but then that's the hallmark of any elite squad.
Vargas' progress under Sampaoli's system was very much thanks to tactics fitting his mould. Should the likes of Joel Campbell, Yaya Sanogo and Serge Gnabry offer background options in the creative and attacking sectors, it only deepens Wenger's ability to utilise numerous shapes and formations.
In terms of sheer scoring stats, Vargas isn't the most impressive candidate, admittedly. The last season in which he netted in the double digits was the Copa Sudamericana, but his performances in Brazil this summer showed what a calm in front of goal the otherwise fiery-tempered technician can be.
For such a fee, the Chilean wouldn't be expected to produce on Sanchez proportions, but his technical ability means that producing similar flashes would be far from a possibility. And considering his age, who knows what Wenger might coax out of the potential purchase in the long term?
The Gunners have already spent big in this window, and signing another big-money superstar may be out of the question.
Having said that, a low-profile move for one of Vargas' potential could be the perfectly understated option that Wenger has been searching for, a player simply looking for a home to nurture the talent so blatantly residing within.