The pair join England duo Owen Farrell and Maro Itoje and Australia's Israel Folau on the shortlist for the award, which will be announced at World Rugby's annual awards dinner in Monaco on November 26.
Barrett capped another impressive season in the All Blacks number 10 jersey.
Compatriot Richie McCaw is the only player to win the award in successive years which he did in 2009 and 2010.
England playmaker Farrell, nominated for the second consecutive year, claimed the European Player of the Year award earlier this year after guiding Saracens to a second straight Champions Cup title.
Sous le choc, Hélène Ségara sort du silence — Scandale Gilbert Rozon
Que cette émission de pur divertissement, et surtout nos merveilleux talents, soit au cœur de tout cela m'a vraiment bouleversée . Pour autant, Hélène Ségara refuse de se lancer dans une chasse aux sorcières.
The England duo make the shortlist after excelling for the British and Irish Lions in the summer's drawn Test series with New Zealand.
Fans can contribute via the World Rugby website.
Ioane only made his Test debut 12 months ago and the rapid wing has been recognised for a magnificent start to his global career, having scored nine tries in 11 matches for the world champions.
Supporters, global captains, coaches and the media will be able to add their voice to the deliberations, before the panel makes the ultimate decisions, with the gongs dished out at World Rugby's annual awards dinner in Monaco on November 26.
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