The Ivorian only joined the Cottagers at the start of last season.
The Ivorian, who joined from Ligue 1 side Nice 18 months ago is currently on loan in Turkey at Galatasaray who, according to the report, would prefer to keep hold of him until the end of the season.
The report claims that Lyon have made two bids of £9.4 million and £10.3 million respectively for Seri but both have been sent back by the Lilywhites.
Fulham are looking for at least £15.4 million, which is what Galatasaray will have to pay at the end of their season to exercise their 'option to buy' clause.
Seri played 32 times for Fulham in the Premier League last season but his performances weren't enough to keep them up. This season, he has played 18 times for Galatasaray in all competitions and has been fairly decent for the Turkish giants.
A move back to France could be tempting for Seri who spent three years there with Nice. Lyon are struggling the Ligue 1 this season and are currently seventh at the moment.
Rudi Garcia's side are badly hurt with injuries and are in desperate need of reinforcements this month.
Seri, a proven commodity in France, would be a very good signing for them and a move certainly makes sense for all parties involved. Seri has no future with Fulham unless they make it back into the Premier League.
Scott Parker's side are currently fourth in the Championship and are unlikely to attain automatic promotion unless Leeds United and West Brom collapse.
The play-off is their most realistic option to return to the top-flight but it won't be easy there either considering that the teams around them have looked really strong this term.
Have something to tell us about this article?