The list also comprises six other players all of whom starred at this summer's FIFA World Cup in Russia, including another France forward, Antoine Griezmann, England's Golden Boot winner for the most goals scored at the tournament Harry Kane and Egypt's Mohamed Salah.
Belgium's midfield duo of Kevin De Bruyne and Eden Hazard were also named among the nominees for the award, with France's Raphael Varane being the only defender to make the list.
Messi scored just one goal for Argentina at the World Cup but had helped Barcelona win both the Spanish La Liga and Copa del Rey. Mbappe became only the second teenager, after Brazil legend Pele, to score in the World Cup final as the Paris Saint-Germain star helped France claim their second title.
The awards ceremony will be held in London on September 24.
Croatia midfielder and captain Luka Modric won the Golden Ball award at the 2018 FIFA World Cup.
Russia hosted its first World Cup from June 14 to July 15 with the games held in 11 cities across the country: Moscow, St. Petersburg, Kaliningrad, Volgograd, Kazan, Nizhny Novgorod, Samara, Saransk, Rostov-on-Don, Yekaterinburg, and Sochi.