Monchi is on a list of names being considered for a newly-created technical director post, BBC Sport's David Ornstein reports.
The former Sevilla goalkeeper has established a reputation as one of football's leading directors, having first transformed the Spanish club's fortunes before moving to the Italian capital.
Arsenal continue to grow confident a deal will be struck, according to The Independent's Miguel Delaney, who also suggests manager Unai Emery has been consulted over the search and has backed his former colleague.
Monchi and Emery combined to lead Sevilla to three consecutive Europa League titles from 2014 to 2016 before both left - Emery following Monchi out the door - in June 2016. The two are believed to have enjoyed a close relationship in Andalucia.
Arsenal have lost CEO Ivan Gazidis and head of recruitment Sven Mislintat in recent months.
Amid the staff turnover, however, one man who is still in his job is Raul Sanllehi, who was appointed director of football following Gazidis' departure, having previously served as head of football relations.
Former Arsenal midfielders Edu and Marc Overmars - currently in technical roles with the Brazil national team and Dutch giants Ajax, respectively - have also been touted as candidates for the new position.