The 18-year-old left-back is wanted by a whole host of top-flight clubs from around Europe - including Juventus, Sunderland, Cardiff and Lyon.
But Arsenal have made their first offer for the France under-19 international, although Le Havre are likely to reject the bid.
The report claims they want at least double the £2.5m offered by the Gunners, who first scouted the youngster when he agreed his first Le Havre contract two years ago.
The attacking full-back has represented France at every youth age group from under-16 through the under-19, and has already made 48 league appearances for Le Havre.
Scouts have been flocking to the northern French club to watch Mendy in action, with Arsene Wenger thought to be keen to secure long-term cover for current first-team left-backs Kieran Gibbs and January signing Nacho Monreal.
Mendy, a 6ft 1in defender, impressed as Le Havre finished sixth in the French second division last term.
He featured 28 times for the club, providing three assists and picking up 4 yellow cards.