And Starsport understands United are lining up a £100m move for Griezmann.
The French superstar opted to stay at Atletico Madrid this year due to their transfer ban but could join next year.
Bale, meanwhile, would also carry a strong commercial appeal if he returned to England from Real Madrid.
According to the Manchester Evening News, executive vice-chairman Woodward is plotting their arrivals.
Paul Pogba and Romelu Lukaku are two of the best examples for United in recent years of commercialism at Old Trafford.
The pair cost £164m collectively, but shirt sales soared to help fund their moves.