And next year’s Old Trafford target is wide midfielder Bale, 27, previously the most expensive player in the world at £86m.
But the Pogba fee would be topped if United could land Bale, who would become the first £100m player.
United believe they could have an ace to play in that their kit sponsors, Adidas, also have a contract with Bale.
And Adidas played a significant role in United’s sensational signing of Pogba.
For this season, though, Bale’s ambition is to win the Champions League again with Real in his home city of Cardiff, where the final will be staged in June.