The Gunners have reportedly stepped up their interest after reports in Turkey suggested Galatasaray were planning a bid of their own in January.
Arsenal were first linked with the Napoli ace last week, and the latest report claims Wenger will sanction a 'preemptive' £12.5m offer in an effort to tie up an early deal for the Switzerland international.
Inler is under contract with the Serie A club through to 2016, but with Rafael Benitez reportedly plotting to bring Lucas Leiva over from Liverpool, it's believed Inler could be available at the right price.
Having said that, Inler's agent previously stated that his client was committed to seeing out his contract.
"Where does Inler's future lie? With Napoli," Inler's agent, Dino Lamberti, said as reported by the Daily Star.
"Yesterday there were reports of me [working on deals for Inler] but I have decided to stop listening to it altogether.
"I also doubt there's already an offer for Inler because if there really is, I would have known about it."
Arsenal midfielder Mathieu Flamini is set to miss matches against Liverpool and Borussia Dortmund and his recent absence has highlighted the Gunners lack of depth in the defensive midfield region.
Mikel Arteta, Jack Wilshere and Aaron Ramsey are all fine central midfielders but none have true defensive instincts like Flamini.
Inler is a tough-tackling, ball-winning midfielder capable of getting box-to-box, and Wenger was believed to be a fan of the Swiss star back in 2011 when he was at Udinese.