The French national football team stars told Canal+ they would love to work together as club teammates, but Griezmann stressed it doesn't mean he is going to Manchester United.
Pogba, who returned to United from Juventus in 2016, has been linked with a move to Real Madrid, while Atletico Madrid's Griezmann was reported to be a transfer target at Old Trafford last summer.
"The whole year together, winning trophies. I really hope we're going to do that one day," said Pogba.
France are among the favorites to win the World Cup in Russia, but they were far from dominant in qualifying, and lost 3-2 to Colombia on Friday, giving up a 2-0 lead.