Both sides are reported to be on alert for the Denmark youth international, who has impressed with his performances for Copenhagen after coming through the youth ranks at the club.
The 6ft 4inch frontman, who is contracted at the Danish side until 2016, has scored 15 goals in 27 appearances this season.
Highly-rated Cornelius is also thought to be on the radar of Inter Milan and Juventus but says he is targeting an eventual move to England.
The 19-year-old told bold.dk: "I think that the Premier League is the best league in the world and I would love to play there.
"It would be like a dream coming true. But there is still a long way and I still have plenty to learn.
"I have a contract with Copenhagen for the next four years so that seems like a good time frame for me, although things change quickly in football so you never know."
Premier League Winner 12/13 Win Outright: Manchester Utd 1/1000
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