The Sun report that the Gunners have compiled a 14-man shortlist for the position, and Faria joins more established names on the list as Arsenal adopt a comprehensive approach in their search for the best man possible.
Arsene Wenger will leave Arsenal in the summer after 22 years at the club and his replacement will be tasked with transforming the club back into Premier League contenders once more.
Faria has worked under Mourinho for 17 years, first as a fitness coach and then as an assistant. Their working relationship dates back to Mourinho's second managerial position at Portuguese club Uniao de Leiria in 2001/02.
It is believed that Faria harbours managerial ambitions of his own, but a job as big as this one may be a step too far for his first solo move.
However, Arsenal owner Stan Kroenke has hired rookie coaches at three of his American sporting franchises - NFL side LA Rams, the NBA's Denver Nuggets and the Colorado Avalanche of the NHL.
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This would indicate that Faria is under serious consideration, though it would be a surprise to many if he were preferred to more established candidates such as Max Allegri, Luis Enrique and Brendan Rodgers.
Mourinho has described Faria as his "methodology right arm, the guy that understands best my information and the way I work." Having worked together throughout their careers, it would be fascinating to see how much Faria has learned from Mourinho, and how Mourinho would cope without his trusted friend.