Tufan, 21, scored only his second goal for his country at Euro 2016 as Turkey beat the Czech Republic 2-0 and played every minute of their two other Group D matches at the tournament.
However, Turkish outlet Fanatik claim that while Liverpool, Tottenham and Everton are all also looking, Tufan himself has chosen the Toffees as his preferred destination.
He is likely to benefit from more first-team minutes at Goodison Park and is also said to be excited about working under new manager Ronald Koeman.
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