The Blues have been linked with a move for the Frenchman all summer but others are said to be interested.
The French youngster has been linked with a move to Goodison Park for most of the summer with it being thought the Blues had made an approach for his services.
However, they may now face competition from both Ajax and Italian side Genoa, with the Daily Mail reports claiming that the Serie A side are pushing the hardest on the Championship side to secure a deal.
Fulham reportedly remain uninterested in any sale and want to keep hold of the French Under-19 international, who impressed in his 15 appearances for the first team last season.
First team recruits more important
A move for Moussa Dembele would make sense on Everton’s part, as they look to sign youngsters for relatively low fees who can be developed for the future.
However, fans may argue that the club would be better served spending their money on proven stars now, with their forward line in particular in need of reinforcement.
The club currently have Romelu Lukaku as the undisputed number one but there is no tangible back up in the squad, with Arouna Kone failing to make the grade so far.