They will join rivals Liverpool in the hunt for the Danish international, whilst Borussia Dortmund are also interested.
Voetbal International report that Everton are aiming for the ambitious swoop as they look ahead to their summer planning.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.