Argentina and Barcelona forward Messi, winner on four occasions, made the shortlist for the eighth time in a row and Portugal's Ronaldo, winner in 2008 and last year, for the fourth time running.
Germany coach Joachim Loew, Real Madrid's Carlo Ancelotti and Atletico Madrid's Diego Simeone were selected for the Coach of the Year award.
The final ceremony will take place in Zurich on Jan. 12.
The FIFA award was founded in 1991 and merged with France Football's Ballon D'Or in 2010.
Germany and Bayern Munich goalkeeper Neuer helped his country win this year's World Cup and often doubled up as a sweeper, rushing out of his penalty area to intercept opponents' attacks.
He is the first goalkeeper to make the final three since compatriot Oliver Kahn was included on the shortlist in 2002.
Italy's Gianluigi Buffon was nominated for the old France Football award in 2006, although at the time that was restricted only to players based with European clubs.
(Writing by Brian Homewood, editing by Ed Osmond)
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