Paris Saint-Germain coach Mauricio Pochettino has told Kurzawa that he is not part of his plans for the club next season.
Kurzawa has tasked his agents with finding him a new club but with a few days left in the window, he is still at PSG this summer.
The defender has reportedly been offered to Crystal Palace where Patrick Vieira is the manager and the club are considering signing him.
But his agents are in talks with multiple clubs and according to French outlet Foot Mercato, they have also proposed him to Lille.
Lille won the Ligue 1 title last season and are in the market for players going into the final days of the window.
Reinildo is their first-choice left-back but he is being pursued by Serie A giants Napoli this summer.
Lille could consider signing Kurzawa if they are forced into the market for a full-back in the coming days.
