Messi was awarded a record-extending eighth Ballon d'Or crown in October in Paris, while Bonmati took the women's prize after starring for Spain in their Women's World Cup triumph.
Erling Haaland and Kylian Mbappe are the other nominees for the FIFA men's best player award, with Bonmati's Spain teammate Jenni Hermoso and Colombian teenage sensation Linda Caicedo also named on the women's shortlist.
The awards ceremony will take place in London on January 15.
The men's finalists were named based on performances from December 19, 2022 until August 20 this year, with the women's decided by achievements between August 1, 2022 and August 20, 2023, the day of the World Cup final.
Messi won his second FIFA best player trophy last year after helping Argentina win the World Cup.
Haaland, who finished second to Messi in the Ballon d'Or voting, scored 52 goals in his first season at Manchester City last term to help the English club to a treble of Premier League, FA Cup and Champions League titles.
France striker Mbappe scored 41 goals in all competitions to help Paris Saint-Germain win Ligue 1.
Bonmati and Hermoso both scored three goals in the tournament as Spain lifted the Women's World Cup for the first time, while Bonmati also won the Women's Champions League with Barcelona last season.
Hermoso was forcibly kissed by then-Spanish football federation president Luis Rubiales following Spain's 1-0 final win over England, sparking a huge controversy and his eventual resignation.
Caicedo, 18, starred in Colombia's run to the World Cup quarter-finals and has since signed for Real Madrid.
