The club is owned by Crystal Palace co-owner John Textor, who was also linked with a takeover of Everton earlier this year.
He was heavily linked with Fulham last summer when he had just one year remaining on his deal.
The two clubs even agreed a fee worth $16m (€15m) but the deal fell through and Cherki ended up signing a new contract.
That means Lyon's valuation has increased to around $26m (€25m) but the club may have little option but to cash in during the January window.
Textor held a press conference on Saturday to provide an update on the club's financial situation and admitted that Cherki ultimately holds all the cards with his future.
"We have resources that go well beyond the club.
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