The Daily Telegraph says Arteta is held in high regard at the Emirates even though he turned down the club's offer of a coaching job to join Pep Guardiola's backroom staff at City.
City's rampant form in the Premier League this season has convinced Gunners bosses even more that Arteta has the coaching credentials to be a success in north London, the paper reports.
Arteta spent five years as a player at Arsenal, including two years as captain, and is still admired by the club's fan base.
He completed his Uefa Pro License earlier this season and is awaiting official confirmation of his final coaching badge.
Arteta's contract at City expires in 2019 – the same time when Wenger's two-year Arsenal deal also runs out.
Guardiola has credited Arteta for Raheem Sterling's improved form this season.
"Mikel Arteta is working many, many days after training sessions for the last action, for the control in the last moment," he was quoted as saying by the Sun.
Wenger, who joined Arsenal in 1996, had faced calls from some sections of the club's supporters to step down during a disappointing 2016/17 season, in which Arsenal won a record 13th FA Cup but failed to qualify for the Champions League.
The Frenchman confirmed at the club's annual general meeting in October that his position as manager will be reviewed by the Arsenal board at the end of the season.
"I want to see what the board thinks of my performance," Wenger was quoted as saying by BBC Sport.
"After that we decide where we go from there. My desire has always been to respect my contracts, but that is what I meant."