The former Juventus midfielder has tolerated a conflicting second season at Old Trafford which saw him drop out of first-team contention severally.
Griezmann, meanwhile, is in talks with his present employers as regards his future but has long been linked with a move away from the Wanda Metropolitano.
According to Don Balon, United are hoping to steal a march on other suitors by offering Pogba to Los Colchoneros in addition to triggering his fellow Frenchman’s €100m (£88.1m) release clause.
Though, the report admits that Pogba is expected to command huge wages, with Atleti coach Diego Simeone not thought to be fanatical on the idea of smashing his club’s wage budget.
Griezmann is now in his fourth season at Atletico, a tenure which has seen him netting 79 goals in 141 La Liga appearances.