Title holder Yaya Toure has been nominated for the sixth consecutive year, along with Pierre-Emerick Aubameyang, Yacine Brahimi and Gervinho.
The winner will be decided by fans of African football, who have until 18:00 GMT on Monday, 24 November to vote for their choice.
The winner will be announced on Monday, 1 December.
Four of the nominees played at this summer’s World Cup in Brazil, where for the first time in the tournament’s history two African sides made it out of the group phase.
Goalkeeper Enyeama played in the last 16 of the tournament with Nigeria, while Brahimi reached the same stage with Algeria.
Enyeama, 32, went into the event off the back of an outstanding campaign for French club Lille – he kept 21 clean sheets for them last season.
In Spain, forward Brahimi’s efforts for Granada led to him being named best African player in the country last term and earning a move to Porto.
Both players carried their excellent club form into the showpiece finals and caught the eye with superb performances – as did Ivory Coast forward Gervinho.
The Roma player has been a revelation in Italy since leaving English Premier League side Arsenal, scoring 10 goals in 39 games for the Serie A side.
He and his compatriot Toure did not make it out of their group in Brazil, but on a personal note both have enjoyed impressive seasons.
Midfielder Toure helped guide Manchester City to their second Premier League title in three years. He also won the Capital One Cup.
Although striker Aubameyang did not play at Brazil 2014 – because Gabon did not qualify – he makes the shortlist for the second year in a row thanks to his club form.
The 25-year-old has settled in his second season with German side Borussia Dortmund and his improvement has been particularly noticeable in the Champions League, where he has already scored three times in the current campaign.
Jay-Jay Okocha is the only Nigerian winner of the award with back-to-back win in 2003 and 2004.