The striker scored 12 goals in 27 appearances for the club last season.
Everton are yet to make a signing this summer under Marco Silva.
Everton centre-forward Cenk Tosun could be the surprise package at Goodison Park next season.
Cenk Tosun joined Everton in the January transfer window.
Reports suggest Everton are considering a move for prolific Sporting Clube de Portugal forward Bas Dost.
Everton striker netted a brace on international duty.
Everton's Cenk Tosun has vowed to improve on his goal-scoring efforts next season.
Sam Allardyce's pragmatic football at Everton not only irked fans, but actually shackled potentially their most dangerous striker since Romelu Lukaku.
Everton beat Newcastle United 1-0 at Goodison Park last night.
The Turkish forward endured a slow start to life in England, but Cenk Tosun now has a record of nearly a goal every other game for Everton.