Neymar finished third in the voting last year but, despite winning three domestic trophies with Paris Saint-Germain after leaving Barcelona, an underwhelming FIFA World Cup on his return from a fractured foot saw the Brazil superstar omitted.
Pogba shone at Russia 2018 as France won the World Cup for the first time in 20 years, but the Manchester United midfielder did not follow international team-mates Mbappe, Antoine Griezmann and Raphael Varane on to the list.
Varane is the only defender included, alongside his Real Madrid colleague Luka Modric - the World Cup's Golden Ball winner.
Mohamed Salah's stunning first year at Liverpool earns the Egypt attacker a place, with Premier League stars Eden Hazard, Kevin De Bruyne and Harry Kane nominated too.
Ronaldo has won the award in each of the two years since the prize was launched, with Messi second on both occasions.
Fans have a chance to vote for their winners, with the victor to be announced at a London ceremony on September 24.
SHORTLIST IN FULL:
Antoine Griezmann (Atletico Madrid and France)
Eden Hazard (Chelsea and Belgium)
Harry Kane (Tottenham and England)
Kylian Mbappe (Paris Saint-Germain and France)
Lionel Messi (Barcelona and Argentina)
Luka Modric (Real Madrid and Croatia)
Cristiano Ronaldo (Juventus and Portugal, Real Madrid in 2017-18)
Kevin De Bruyne (Manchester City and Belgium)
Mohamed Salah (Liverpool and Egypt)
Raphael Varane (Real Madrid and France)