The Cameroon international has been a targeted by the Toffees to partner Romelu Lukaku and the striker is keen to link up with new boss Ronald Koeman.
Aboubakar, 24, bagged 16 goals last season and has netted 13 times in 45 games for his country.
And Oumar Niasse and Arouna Kone have struggled to make a name on Merseyside in the shadow of Lukaku.
Goodison Park chiefs are keen to keep hold of their star man Lukaku, 23, with Juventus having scouted the Belgian at Euro 2016.
Chelsea are also after the hitman — who they sold to the Toffees back for £28m in 2014 — as Antonio Conte looks to rebuild the squad at Stamford Bridge.