Kuzawa, 27, has been expected to join the mass exodus of PSG players leaving at the end of their contract.
But PSG want to hold on to French international Kurzawa, offering him an unexpected four-year deal.
Sporting director Leonardo had shown little motivation to renew Kurzawa previously, but has suddenly changed his stance.
Kurzawa’s camp reportedly ‘totally surprised’ by the offer, as they had begun looking for a new club.
They responded to Leonardo by asking for a huge pay rise for Kurzawa which would double his current salary.
The two sides have given themselves until mid-July to see whether or not they can agree terms.
Chelsea renew interest
If the discussions stall, another deal is on the table: a two-month extension to allow Kurzawa to see out the season.
Cavani and Meunier have already rejected such deals and will play no part in PSG’s remaining Champions League games.
PSG’s U-turn has given the former Monaco star a decision to make – move abroad or continue his Parisian adventure.