According to reports, formal talks have started between David and two Premier League teams - Aston Villa and Tottenham.
Tottenham sees David as a potential replacement for Harry Kane, who left the team two years ago to join Bayern Munich.
Aston Villa, on the other hand, is considering David as an option due to uncertainty over whether Manchester United's Marcus Rashford will join the team permanently.
David has been with Lille for five seasons and will be leaving the club when his contract expires.