The south London club want to sign a striker before Deadline Day on Tuesday and Edouard is their top choice.
Palace were also in talks for Arsenal's Eddie Nketiah, but a deal is now looking unlikely as the two parties are far apart of their valuation.
Edouard, 23, has been trying to leave Celtic since last summer.
The Frenchman could finally get his wish before Tuesday's transfer deadline.
He has scored 77 goals in 150 appearances for the Bhoys.
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