Memphis could allegedly be allowed to leave for around €30m (£27.5m) during this summer's transfer window as his contract in France is due to expire next June.
According to Sky Italia, Milan are now ahead of Barca in the race for the Netherlands international, who could be used in a swap deal for Lucas Paqueta.
Memphis has been in excellent form for Lyon at the start of the new Ligue 1 campaign, scoring four times in three appearances, including a hat-trick against Dijon on the opening weekend of the season.
The Dutchman has allegedly made it clear that he will not be signing a new deal with Les Gones. body check tags ::