Griezmann, 27, has been linked with a move to the Premier League giants, as well as La Liga leaders Barcelona, having revealed earlier this week that he intends to iron out his future prior to the World Cup.
"My future will be decided before the World Cup, I want to go to Russia with a clear mind, I think that's what everybody wants, it's not so much the question of where I'll play, which may be boring, but about having the peace of mind if I'm still in one place or another," he said.
"I've told my sister that, whether I stay or not, I'll have to decide before (in reference to the World Cup)."
And while the forward believes it would be great to play with France team-mate and United star Pogba every day, he played down a possible switch to Old Trafford.
"If we could have this every day," Pogba said on Canal+ as the pair interviewed each other.
Griezmann responded: "It would be nice.
"But beware, that doesn't mean I want to go to Manchester United."
Griezmann has scored 23 goals in 38 games in all competitions for Atletico this campaign in what is his fourth season at the club.
Pogba, meanwhile, has faced criticism for his displays for Jose Mourinho's United.