Madrid are studying the possibility of making a move for Fekir, as they are on the hunt for an offensive midfielder who could play a similar role to Luka Modric in the future.
However, Fekir continues to be linked with a move away from the club and with just over 18 months remaining on his contract, it appears that Lyon have chose to entertain receiving the highest-possible fee for the player.
It is not clear if Madrid is interested in signing Fekir, who was close to completing a transfer to Liverpool last summer.
He was linked with a move to Stamford Bridge in the summer but joined Milan in a £16.3m loan deal, with the club having an option to buy him permanently for £32.6m.
Is Fekir a good option for Chelsea?
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The Blues are now in fourth place in the Premier League table and 11 points behind leaders Liverpool FC. Alvaro Morata has been disappointing up front this year and Olivier Giroud isn't an everyday striker anymore.
For now, those in charge are focused on agreeing a deal for Exequiel Palacios from River Plate, with an agreement seeming further away with every passing day.
Santiago Solari has steadied the sinking ship that Real Madrid was.
Fekir has also been linked with Real's rivals FC Barcelona previously, but if Los Blancos were to launch a formal bid for the 25-year-old, they would be strong favourites to land his signature. Nevertheless, deals for the likes of Neymar and Mbappe are highly unlikely in the January transfer window. Higuain also earns more than Morata's £140,000-a-week Chelsea wages.