The Serie A side are reportedly happy to allow the Poland international, valued at roughly €30m, to leave with Rafael Leao and new recruit, 38-year-old Zlatan Ibrahimovic, ahead of him in the pecking order.
Injuries to Harry Kane and Wesley Moraes have forced the two clubs into action during the January transfer window, with both lacking in terms of depth without their first-choice strikers.
Sky Italia now report that both clubs have put in bids thought to be in the €30m mark for the 24-year-old, per Calciomercato.com, with a Premier League move seemingly imminent one way or another.
Piatek originally turned heads when he first arrived in the Italian top flight, scoring 12 goals in his first seven games for Genoa.
After less than six months, Milan acted quickly to bring him to the San Siro, where he made a similar impact with seven goals in his seven appearances for the Rossoneri.
But his impact has since diminished with just four goals in 18 appearances this season, with fallen giants Milan currently sitting 10th in Serie A.
Still, he averages a respectable tally of 26 goals from 55 Serie A appearances overall.
Piatek was an unused substitute in Saturday’s 2-0 win over Cagliari, in which both members of their front two, Leao and Ibrahimovic, both getting on the scoresheet in his absence.