Parma, a Serie A club, is looking for a new coach after their previous manager, Cristian Chivu, joined Inter Milan.
Chivu successfully guided Parma to safety last season on a short-term contract.
Parma have already contacted Arsenal to ask for permission to speak with Cuesta, who is 29 years old.
However, Arsenal has not yet responded to the request.
Cuesta has been working with Arsenal manager Mikel Arteta since Arteta took over in 2019.
He was also a candidate for the Norwich City job at the end of last season.
