The 19-year-old has recently been linked with the likes of Arsenal, Liverpool, Manchester City and Barcelona.
The Daily Star reports that United have now joined the race for the youngster and manager Sir Alex Ferguson is ready to bid more than £20mllion to land the Denmark international.
A source told the Daily Star Sunday: “United are hot on him. Trust me, they want him and £20million is the price being bandied around.
“Yet ironically both Chelsea and Spurs turned him down several years ago because they thought he was too small. He has since turned into a world-class player.”