The Gunners have been on the hunt for a left-back this summer to provide competition for Kieran Tierney, who signed a new long-term contract last week.
The club have now opted to press ahead with a move for Tavares and they are finalising a deal for the 21-year-old.
Arsenal are set to pay around £7m up front for Tavares, with Benfica due to bank more money in the form of add-ons. Any deal, however, is not expected to be worth more than £8.5m in the end.
Personal terms with Tavares have all been agreed too and the full-back just needs to undergo a medical before sealing a move to Emirates Stadium.
The Portugal Under-21 international’s arrival should pave the way for Sead Kolasinac, who spent the season on loan at Schalke, to leave the club during the current transfer window.