The on-fire forward, 18, signed a new four-year contract at Old Trafford in October - and has already scored 15 times this season.
The Sun reports Andy Mitten, a Man Utd journalist for The Athletic, revealed the secret offer, telling the Talk of the Devils podcast: "I think [Greenwood] can be a world class player.
"I know that there has been offers for him.
"Go back a year and Juventus were prepared to offer his family life-changing amounts of money.
"Manchester United deserve credit for the way they got him to sign a new contract."