In total 30 nominees will be announced, with the ceremony scheduled for 3 December.
No City player has won the coveted prize and Lionel Messi and Cristiano Ronaldo have dominated the award over the past decade, winning it five times each.
Federation Internationale de Football Association split from the Ballon d'Or in 2016 to launch its own set of awards.
The 31-year-old highlighted his current tendency to make mistakes when he gifted Croatia a goal during the World Cup final.
Having finished third in 2016, Griezmann, who won the Europa League last term with Atletico as well as lifting the World Cup with France over the summer.
Bulgarian arrested in Germany, charged with journalist's murder
The journalist's murder shocked her country and prompted claims she may have been targeted as "a warning" because of her work. A TV reporter who covered European Union funds fraud cases was brutally murdered and allegedly raped in northern Bulgaria.
Aaron Ramsey's goal that marked "the return of Gunners"
They made it hard for us to play but we knew if we kept playing we would score so everyone is happy today. And don't look now, but Arsenal has won nine games in a row under Unai Emery and are flying high.
What Pogba Said To Mourinho During Half-Time vs Newcastle
"If we had been against any other team but Barcelona - we don't know - but you would have fancied us to win those games". Mourinho also made a gesture with his right hand while speaking, pointing with his little finger.
England only have one representative on the list in Harry Kane while Gareth Bale is also among the nominees.
Having lost out in the Federation Internationale de Football Association best player of the year award to Luka Modric, Cristiano Ronaldo takes his place among the 30 nominees for the Ballon d'Or that were being unveiled in stages throughout Monday.
"The best team in the world surely possesses the best player, right?"
The Manchester United midfielder was named on the 30-man shortlist for the award for the best player of the year, with the victor to be announced in Paris on December 3. The victor of the prestigious Ballon d'Or organised by France Football magazine will be announced on December 3.