The France international has regularly been linked with a move away from the Vicente Calderon following his superb form in the past 12 months, with United and Paris Saint-Germain among those most regularly rumoured to be interested.
Griezmann and Pogba have posted a number of pictures together on social media, with the latest showing them returning to their France training base on the back of a golf buggy.
The duo's friendship has frequently been cited as a key factor in any attempt by Jose Mourinho to tempt the Euro 2016 Golden Boot-winner to Old Trafford.
While Griezmann insists he is happy with life at Atletico and is not actively looking for a move, he has suggested the chance to play alongside Pogba at club level in future could be tough to turn down.
"A future transfer depends on how I feel," he told Sky Sport in Germany. "Right now I'm a father so a move to another city would not be the right thing. I'll see if I want to do something else in the future, though.
"Right now I'm very happy at Atletico and I still want to win trophies with this club.
"I always ask Pogba about United. I think Manchester United is a huge club with a really good infrastructure. I ask Paul about some of the players - if they're really that good and if Mourinho's really that good.
"You hear a lot but in the end it's the same with United as it is with PSG. Right now, I don't see me moving to a new club. It would be awesome to play together with Paul one day."