The 26-year-old is out of contract in the summer and is attracting interest from the Premier League club.
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The attacker is seen as a potential replacement for West Ham-bound Danny Ings.
Dembele progressed through the youth ranks with Paris Saint-Germain before leaving for Fulham in 2013 at the age of 16.
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While scoring 19 goals in 64 appearances for the west London side, the striker really found his feet at Celtic where he bagged 51 goals in 94 appearances before earning a move back to France with Lyon in the summer of 2018.
Dembele has managed 159 appearances for Lyon in that time, but after being limited to just 14 appearances and two goals this term, it means that his future is in doubt.
With a contract that expires this summer, it's unlikely that the 26-year-old will look to extend his contract at the club, meaning that he could be available for a cut-price fee this month.
Ings is on the cusp of a move to West Ham after the two clubs agreed a £15million fee with the striker to undergo a medical in east London.
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With that deal for Ings all-but done, it means that Unai Emery may have already lined up a proven, but cost-effective solution to their striking woes.