However, the toffees are not the only club in the hunt for the Turkish international as former club Arsenal have also shown an interest.
The North London club got rid of Ozyakup in 2012 for just £400,000 but have kept tabs on the player who has become a key member of the BJK team that has won back to back titles in Turkey.
It is believed that Arsene Wenger sees the player as a possible replacement for Mesut Ozil, who is yet to sign a contract extension amid rumours that he may leave in the summer.
The Gunners will hope that they can beat their Premier League counterparts to the signature of the player, but the negotiations with Ozil may leave the club on the back foot should they need to replace the German.
Ozyakup could be a good replacement for Ozil having scored 5 goals and assisted a further 10 last season.
A source in Turkey has said that Everton have been given permission to talk to the player over a potential move in January. The deal could potentially help bolster a squad that has underwhelmed in the first part of the season despite spending big on 9 new players last summer.