The Gunners are in talks with the Ligue 1 champions for the France international left-back, who has just six months left on his current contract.
Negotiations are believed to now be at an advanced stage between the two clubs.
Arsenal are pushing to get a deal done for a fee around £6m for the 27-year-old, who moved to PSG from Monaco in 2015 in a deal worth close to €22million (£16m/$25m).
Since then he has won three league titles while at Parc des Princes, as well as three Coupes de France and three Coupes de Ligue.
Although Kurzawa started for PSG as they claimed a 4-1 win at Monaco, it was only his 13th appearance in all competitions this season.