Joining the 24-year-old on this year's Ballon d'Or shortlist, which was gradually revealed in stages by France Football on Monday (9 October), is a pair of Liverpool attackers in Sadio Mane and Philippe Coutinho, remarkably consistent Manchester United goalkeeper David De Gea and influential Chelsea playmaker Eden Hazard.
Neymar, who left Barcelona to join PSG this summer in a world-record move, came third in the voting in 2015 and was fifth a year ago, while Suarez has yet to make it into the final three-man selection.
The fourth and fifth batches of nominations released by award organisers France Football included Barcelona star Messi and Atletico Madrid's Griezmann, who finished second and third respectively in 2016. The Argentine topped the winning list with five times.
The trio are joined by annual candidates Lionel Messi and Cristiano Ronaldo.
Ronaldo came off the bench to help Portugal snatch three points from minnow Andorra, but the team still needed to beat leaders Switzerland on Tuesday for an automatic qualification to Russian Federation.
Real Madrid took up seven nominees including Ronaldo.
The Spain no.1 has enjoyed a fine year for club and country and, last week, confirmed a place at the World Cup finals with another clean sheet - in a win over Albania.