The 28-year-old has struggled with injuries which has limited his impact for the Toffees over the past couple of seasons.
He has scored 71 goals in 273 games for the club, but could only register three goals and three assists last season in 26 appearances.
Everton struggled for goals last season, scoring 42 in 38 Premier League games, and Moyes needs to add more firepower to his ranks ahead of their first season at the brand new Hill Dickinson stadium.