Real Madrid star Ronaldo is favourite for the crown after winning the Champions League and also Euro 2016 with Portugal, even though he exited the final win over France with an early injury.
Perennial rival Messi of Barcelona and Argentina, the reigning player of the year, had a less stellar year by his exacting standards.
Griezmann suffered double heartache with France and Atletico Madrid at Euro 2016 and in the Champions League final.
German Olympic champion Melanie Behringer will go up against Brazilian veteran Marta and US star Carli Lloyd for the women's accolade.
Real Madrid's Zinedine Zidane will vie with Leicester miracle worker Claudio Ranieri and Portugal boss Fernando Santos for the title of top coach.
Despite benig a relative coaching novice, Zidane led Real to the Champions League title after replacing Rafael Benitez mid-season at the Bernabeu.
Ranieri shocked the football world when he led Leicester to a first ever league crown in England while Santos ensured Portugal finally broke their major title duck.
"I am getting better day by day and continue to learn. But maybe it is too early for me to be up there among the three nominees," Zidane reflected modestly.
The title of best women's coach will go either to US coach Jill Ellis, Germany's Silvia Neid or Sweden's Pia Sundhage.
The awards ceremony takes place in Zurich on January 9, 2017