Ivory Coast midfielder Toure became just the second man to win the prestigious CAF award for a third consecutive year last January, and is now in line to win an unprecedented fourth straight award.
Abedi Pele of Ghana won the award three times in a row under its previous guise of France Football's African Player of the Year from 1991.
Toure's nomination is recognition of a superb domestic year with Manchester City that saw him collect the Premier League title and the League Cup.
The 31-year-old scored 20 goals in 35 Premier League appearances for Manuel Pellegrini's side in the 2013-14 campaign, as they held off Liverpool's challenge by two points.
Aubameyang enjoyed a fine debut campaign at Borussia Dortmund last season, wowing fans with his direct running and lightning pace.
The Gabon international scored 13 Bundesliga goals last term to help Jurgen Klopp's men to a second-placed finish and the DFB-Pokal final.
Nigeria captain Enyeama skippered his country at the World Cup in Brazil earlier this year.
The 32-year-old was an ever-present in a Lille side that finished third in Ligue 1 last term, helping the club to the UEFA Champions League preliminary stages where they lost to Porto.
Ghana's Asamoah Gyan and Nigeria's Ahmed Musa were previously on a five-man list, before that was whittled down to three on Thursday.
The winner of the gong will be announced at a ceremony in Lagos on January 8.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
