Despite Cristiano Ronaldo, Lionel Messi and Luka Modric, who won the Golden Ball in the World Cup, and was also voted as FIFA's best player last month, Griezmann remained adamant that a France worldwide should be given Ballon d'Or.
The Kopa Award will be voted upon by the 33 surviving winners of the Ballon d'Or, among them Cristiano Ronaldo, Leo Messi, Zinedine Zidane, Ronaldinho, Ronaldo, Luis Figo and George Weah.
What is the Ballon d'Or?
Portugal forward Cristiano Ronaldo, who joined Juventus from Real Madrid in the summer, won last year's Ballon d'Or.
Wales worldwide Gareth Bale, scorer of a brace in Real's European final win over Liverpool, is among the 10 names already released.
Manchester City striker Sergio Aguero and midfielder Kevin de Bruyne are also contenders, as are Liverpool goalkeeper Alisson and forward Robert Firmino.
Kylian Mbappe and Antoine Griezmann, two key members of the France national team that sailed to their second-ever World Cup trophy are also likely to finish with high tallies, as are Eden Hazard and Kevin de Bruyne, members of Belgium's star-studded side that came third at Russian Federation 2018.
Other nominees are Pernille Harder, Lindsey Horan, Fran Kirby, Sam Kerr, Lieke Martens, Megan Rapinoe and Christine Sinclair.
Kante played alongside Pogba in central midfield at the World Cup and were a key part of France's success at the tournament.
For six years it combined with world football's governing body to become the Fifa Ballon d'Or.