Palace have had one offer for the 19 year-old rejected by Angers this month.
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And now Championship club Wrexham have made their move with a bid of their own.
The Daily Mail says Wrexham have offered £12m plus £2m in bonuses for Cherif.
In contrast, Palace's last offer was for a loan to buy arrangement. The Eagles bid a £2.6m loan fee for the remainder of the season with an option to buy worth £13m.