The winner will be announced a week later on 17 December on the BBC's African sports programme Fast Track.
Both Sunderland striker Gyan and Marseille midfielder Ayew starred for Ghana as they reached the quarter-finals of the World Cup for the first time.
The 29-year-old forward Eto'o played a vital role as his Italian side Inter Milan won the Champions League and a domestic double.
English Premier League side Chelsea secured the a league and cup double for the first time in their history, thanks in part to the goals of 32-year-old striker Drogba.
While, Toure, 27, became the highest-paid footballer in English football following the midfielder's move from Barcelona to Manchester City.
The shortlist was determined by a panel of experts across Africa who took into consideration individual skill, technical ability, teamwork, consistency, impact on results and fair play.
"It has been a significant year for African football, with the World Cup being hosted in the continent for the first time and Angola hosting the Africa Cup of Nations," said BBC Fast Track presenter Farayi Mungazi.
"A youthful Ghana side lit up the World Cup so it is great to see the Black Stars duo of Asamoah Gyan and Dede Ayew receive their first nominations as well as the ever classy Eto'o, Drogba and Yaya Toure."
Last year's winner was Drogba of Chelsea and Ivory Coast after his consistent form and goals for club and country.
Previous winners of BBC African Footballer of the Year award:
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