The left-back will be out of contract at the end of the current campaign, and as things stand there is no sign of him penning a new one with the Ligue 1 champions.
The 27-year-old will be free to talk rival clubs in January with a view to agreeing a free transfer for the end of the season, but PSG would rather cash in on a permanent basis.
Coach Thomas Tuchel would like to use the money raised from any sale to strengthen his own squad and is keen to get the defender out of the door in January.
The France international has made 100 appearances for PSG following his move from Monaco, scoring 12 goals in the process, but he has slipped down the pecking order in this campaign.
He has made just seven appearances for Tuchel this season and is keen to move on in search of more regular first-team football.
Kurzawa will not be short of offers and now has a decision to make over whether to move in January or sit tight until the summer when the offers may be more lucrative.
There is already talk that a number of English Premier League clubs are in the hunt and are ready to offer him a route out in the new year.
Much could depend on the fee PSG will ask for and whether anyone is willing to match it when he will be available on a free just a few months later.