The Gunners are planning to sign a marquee striker this summer and they have been linked with several names.
They have a strong interest in Sporting CP star Viktor Gyokeres, but reports claim that the club have other plans.
It is reported that contact has been established with David, who has bagged 25 goals and 12 assists for Lille this term.
David has been a long-term target for Premier League teams but none have been preferred to meet the asking price.
Lille are not set to lose him on a free transfer, considering he has no plans of extending his contract beyond June 30.
West Ham United have been in regular contact with the player's entourage and Arsenal could hijack their pursuit.
David is a genuine goalscorer but there are still questions about whether he can cope with the physical demands of English football.