Pep Guardiola would be reluctant to stand in Mikel Arteta's way if he had the "privilege" of being offered the Arsenal job.
Arteta finished his playing career with the north London club in 2016 before joining Guardiola's backroom staff at City.
The Gunners are on the lookout for a new head coach after Unai Emery was sacked in the aftermath of a 2-1 Europa League defeat to Eintracht Frankfurt that extended their winless run to seven matches.
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Arteta has become an increasingly influential member of Guardiola's coaching team, especially since long-time confidant Domenec Torrent left to take charge of MLS side New York City last year, and Raheem Sterling has credited extra sessions with the ex-Everton midfielder for aiding his rapid development.