French website BuzzSport reports that the Blues are considering making a £110million move for the duo.
Chelsea may finance the deal through the sale of French midfielder Eden Hazard to Spanish giants Real Madrid.
The Blues have long been linked with Griezmann and they could be ready to trigger his £46million buy-out clause.
Chelsea are also ready to join Spanish giants Barcelona in the battle to sign former Manchester United midfielder Pogba from Juventus next summer.
Reports claim Pogba would cost Chelsea in excess of £64million.
