The Gunners were interested in the Switzerland midfielder two seasons ago before he moved from Udinese to Napoli. But the report claims Wenger is ready to renew his interest in the January window after Inler's impressive start to the season.
Now managed by former-Liverpool boss Rafael Benitez, Inler has played an important role in the team's rise to second in the Serie A table.
The 29-year-old defensive midfielder has been identified as a potential January addition, with Wenger blessed with attacking midfield options but short of box-to-box tacklers.
Mathieu Flamini is the club's current first-choice holding midfielder, but he has struggled with injury in recent weeks. He hasn't played more than 25 games in a season since 2009, and faces up to two weeks out with a groin injury aggravated against Norwich.
The report claims Wenger would be willing to pay up to £12.5m for the Swiss star, but with Galatasaray also interested he could be priced out of a move.
Roberto Mancini is expected to be busy in his first transfer window as Galatasaray boss in January, and the Turkish giants have been monitoring the Arsenal transfer target.