Lyon right-back Bronze was named UEFA Women's Player of the Year last week but faces stiff competition from Rapinoe and Morgan to claim the global accolade.
Rapinoe, 34, looks to be the frontrunner after spearheading her country to Women's World Cup glory earlier this year.
Team-mate Morgan netted the same number of goals in France, including the winner in the 2-1 semi-final defeat of England, and only missed out on the goalscoring crown by virtue of playing more minutes than Rapinoe.
Bronze's hopes could hinge on a strong club campaign as she helped Lyon to the treble, although two of the previous three winners - Carli Lloyd and Marta - have been based in the NWSL in America.
Similar battle lines have been drawn for the title of The Best FIFA Women's Coach, with England manager Phil Neville in contention against Jill Ellis, who has won back-to-back World Cups with USA.
Netherlands boss Sarina Wiegman is the other contender after leading her country to the World Cup final.
Christiane Endler, Hedvig Lindahl and Sari van Veenendaal are the finalists for the goalkeeper's gong.
All award winners will be announced at a ceremony in Milan on September 23.