The 20-year-old has scored 20 goals this season for Danish side FC Copenhagen.
Everton has been keeping an eye on the striker for months.
Cornelius said: “It’s a big pat on the back that Everton are watching me “I know the club, I’ve seen them a few times and the Premier League is a great competition.”
Copenhagen sporting director Carsten Jensen said: “Cornelius is in our plans for next season — but anything is possible.”
Arsenal, Stoke and QPR have also shown an interest in the £5million-rated striker.
