The Mirror says Borussia Dortmund are among those interested in the Dutchman. Clubs from Spain, Turkey, England and the Netherlands are also said to be keen.
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Arne Slot himself now wants to push ahead with an extension with Van Dijk. The captain's future is the top priority for the incoming manager, who will take over at Anfield.
Slot will leave Feyenoord to succeed the departing Jurgen Klopp this summer.