Kurzawa, 27, is out of contract with PSG this summer so is free to talk to overseas clubs about a summer move.
But Arsenal may decide to move for him in the January transfer window following positive talks with the player.
The Gunners signed left-back Kieran Tierney for £25million last summer, but the 22-year-old is currently sidelined with a shoulder injury and it is unclear when he will return.
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