The striker only moved to the Premier League club last summer under boss Sean Dyche.
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However, Fotomac states that talks are underway between the two clubs over a deal.
Beto is in line to move to Turkey, as manager Jose Mourinho wants him at Fener.
Everton were not eager to sell, but will recoup a big fee of €20 million for the striker.
The Toffees are likely to sign a replacement striker to ensure they have adequate cover for Dominic Calvert-Lewin.