Cuesta is sought by the Serie A Club Parma.
Parma is looking for a new coach after losing Cristian Chivu to Inter Milan. The Romanian successfully lived away from relegation with a short -term contract last season.
Parma has already approached Arsenal for permission to speak with Cuesta, 29, although the Gunners still have to respond, says De Spiegel.
Cuesta was also a candidate for the job in Norwich City at the end of last season.
The Spaniard has been in Arteta's staff since the appointment of the latter in 2019.