L'Equipe says Arsenal face paying up to £6million to sign Kurzawa.
Kurzawa, 27, is out of contract at the end of the season and is free to talk to foreign clubs this month.
Arsenal have held talks with agent Kia Joorabchian over a deal for the left-back but would be interested in signing him this month.
PSG are willing to let Kurzawa depart and will look to get a small fee for him, rather than lose him for nothing in the summer.
Arsenal will have to pay between £4.2m and £6m if they are to sign Kurzawa during the transfer window.