The Cottagers plan to pursue the 20-year-old in the summer. They are already anticipating high-stakes negotiations with his agent, who is Kylian Mbappe’s mother.
Fulham were one of the busiest clubs on transfer deadline day as they sought to bolster their squad for manager Marco Silva.
They attempted to hijack Lyon’s move for West Ham United attacker Said Benrahma, but he had his heart set on a move to Lyon.
The Hammers also rejected their proposal, which was a straight loan rather than an outright sale.
Fulham then turned to Lyon, who needed to sell players to balance their books after moves for Benrahma, Nemanja Matic and Orel Mangala.
However, it seems they made their move too late and will need to wait until summer rolls around to snap him up.
Cherki, a highly-touted talent, can play across the forward line. He is not explosive but has the ‘X-factor’ in the final third and can create chances for fun.
He was a target for Chelsea last summer before they signed Cole Palmer, and Fulham will be hoping they do not re-enter the mix for the French youth international this summer.
Elsewhere, Chelsea have agreed for Armando Broja to join Fulham on loan for the rest of the season.
Fulham will pay £4 million for the Albanian international, who is looking for a run of games in the first team.
Wolverhampton Wanderers and West Ham were also interested, but Fulham won the transfer race as they looked for a replacement for former captain and talisman Aleksandar Mitrovic.
Broja has bagged two goals and two assists in 19 appearances this season.
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