Cuesta is wanted by Serie A club Parma.
Parma are seeking a new coach after losing Cristian Chivu to Inter Milan. The Romanian successfully guided Parma away from relegation last season on a short-term contract.
Parma have already approached Arsenal for permission to speak with Cuesta, 29, though the Gunners are yet to respond, says the Mirror.
Cuesta was also a candidate for the Norwich City job at the end of last season.
The Spaniard has been on Arteta's staff since the latter's appointment in 2019.
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