Foot Mercato says former Nice boss Patrick Vieira is ready to dip back into the French league market and try to sign the left-back, who has drawn attention in the past from Manchester United, Chelsea, West Ham and Spurs.
And sources in the French capital claim Kurzawa's advisors have offered him to Palace.
The deposed serial champions are expected to seek around £11million for him.
Born at Frejus on the French Riviera, he spent eight years with Monaco before a £20m move to the Parisians.
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