Konsa remains Arsenal's first-choice defensive target, but the Premier League champions are yet to meet Aston Villa's £60m valuation of the 28-year-old.
BBC Sport reported last week that Arsenal had reopened talks over a deal but still fell short of an agreement at that stage, prompting the Gunners to briefly turn their attention to Bayer Leverkusen's Jarell Quansah before refocusing on Konsa amid a growing sense the transfer will now get done.
Konsa joined Aston Villa from Brentford in July 2019 and has made 286 appearances for the club across the past seven seasons. He featured 48 times in all competitions last term, scoring twice and adding an assist, as Unai Emery's side won the Europa League and finished fourth in the Premier League to secure Champions League qualification for 2026-27.
The versatile defender, who can operate at centre-back or right-back, has not featured at all in Villa's pre-season, including the 2-1 defeat to Paris Saint-Germain in the UEFA Super Cup, after Emery granted him four weeks off following the World Cup. Konsa played every minute of England's run to third place at the tournament.
Arsenal's need for defensive reinforcements has been sharpened by fitness problems affecting William Saliba and Jurrien Timber, leaving Mikel Arteta short of senior options at centre-back heading into the new season.
Villa, for their part, are said to be reluctant to lose Konsa, but with two years left on his contract, face a decision over whether now is the right time to cash in on one of their most experienced defenders.
Arsenal's interest has been ongoing throughout the window, with an initial approach worth around £30m rejected by Villa earlier in the summer. That gap between the two clubs' valuations has narrowed only gradually, though reports in the past few days suggest talks have reached a more advanced stage, with Konsa said to have already agreed personal terms should a fee be settled.
Should the move go through, Konsa would become the latest defensive addition at Emirates Stadium this summer as Arteta looks to shore up a squad already chasing a domestic and European double.