The 27-year-old was part of the France team that claimed World Cup glory in the summer, with head coach Didier Deschamps steering Le Bleus to their first title since 1998.
It has not been completely plain sailing since the tournament in Russia, however, with France having been beaten by Netherlands in their most recent Nations League fixture, while they were held by Iceland in a friendly in October.
And although Griezmann believes Deschamps has done a "terrific" job and earned the right to remain in charge of the national team for as long as he wants, he believes former Real Madrid manager Zidane would be the ideal choice to take over.
"I don't know how long Deschamps wants to remain as national manager," he told ESPN.
"He has earned the respect he has, and I think he will be on the job as much as he wants. However, I believe Zidane could be the best manager available [for France]. Actually, Deschamps has done a terrific job."
Regardless of who is in charge, Griezmann says that France are targeting further glory at Euro 2020, and then even the 2022 World Cup, given the youth withing the squad that includes the likes of 19-year-old Kylian Mbappe.
"I think our average age [at this past World Cup] was 25 years, or it was around that. It was a very young squad. I think we have the players and, above all, the youth in order to do something bigger.
"The Euro is coming, there is another World Cup in store and, if we keep on doing our job this way, staying humble as we are, we can hope to win it all."
And the former Real Sociedad forward claims he didn't want anything to do with football for a period after those agonising defeats, and that he couldn't cope with watching any football on television for a while.
He said: "The first week [after the Euro final defeat] was so tough, I didn't want to know anything about football.
"I couldn't bear myself to watch matches on TV. [Highlights of] the France matches were on, [discussion of] the Champions League final was on and I couldn't watch TV.
"I tried to be inside my world, with my parents, in my hometown, with my wife ... and not much else. I didn't want to know anything about it."