This is according to Barcelona-based newspaper Sport, who understand that Wenger wants Busquets as an upgrade on Francis Coquelin.
The report adds that Arsenal are able to afford the Spain international, although it seems the chances of the Gunners successfully luring the midfield enforcer to the Emirates Stadium this summer are extremely slim.
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Busquets recently extended his contract at the Camp Nou until 2019 and remains one of Barcelona’s most important players.
Once underrated by some, and widely criticised because of his on-field theatrics during certain high-profile matches, Busquets is now universally regarded as one of the best holding midfielders in world football.
Barcelona would be crazy to sell Busquets
Barcelona boss Luis Enrique will have no desire to offload the 27-year-old, whose ability to play a successful pass has been second only to the legendary Xavi Hernandez in recent seasons, and it would take an astronomical fee to even tempt the Catalan giants into selling the midfielder.
But even if Arsenal were to offer a club-record fee - Mesut Ozil, who cost £42.4 million in 2013, remains the Gunners’ most expensive signing to date - Barcelona would almost certainly reject the offer.
Barça are not as solid without Busquets, who protects his team’s defence with impressive effectiveness, and would be foolish to weaken themselves by selling the World Cup winner to Arsenal.
One way the deal could make any sense
The only way the deal would make any sense from a Barcelona perspective is if they sign a replacement first.
Paul Pogba could be that man. It was reported earlier this summer that Barcelona have reached an agreement to sign the Juventus midfielder for next summer, six months after their transfer ban expires.
Barcelona are also reportedly close to signing the highly-rated Brazilian youngster Gerson who, incidentally, has been likened to Pogba.
But even then, Busquets is arguably better than both Pogba and Gerson, and is approaching the peak years of his professional career.
That Arsenal want to sign Busquets should come as little surprise - but that Wenger believes the Spaniard might be obtainable is a little bizarre.
Wenger managed to sign Ozil and Alexis Sanchez - from Real Madrid and Barcelona, respectively - because they were not deemed indispensable by their previous employers.
It’s a different story for Busquets, though, who has a key role to play for Barcelona over the next few seasons.
Arsenal fans: do you believe this report is true? Would you even want Sergio Busquets if it was? Have your say by leaving a comment in the box below!