The 21-year-old made 19 appearances in all competitions for Benfica last season and is being viewed as back-up for Kieran Tierney, who signed a new long-term contract last week.
Talks between Arsenal and Benfica are understood to be progressing, with discussions centered around a price of around £7 million ($9.72m).
Nothing has been agreed yet, with talks continuing, but Arsenal is hopeful of getting a deal done for the young full-back, who is also attracting interest from other clubs across Europe.
The Gunners have prioritized bringing in another left-back this summer as cover for Tierney and have previously looked at the likes of Ryan Bertrand and Patrick van Aanholt.
Tavares made a brief substitute appearance against the Gunners last season during Benfica’s 3-2 defeat in the Europa League knockout stages.
What sort of left-back is Tavares?
Tavares is viewed as a strong attacking left-back, who has excellent pace and athletic qualities.
He is prone to the occasional error defensively, however, that would be an area Arsenal would look to develop him should he complete a move to north London.