The Spanish giants want to pay closer to £100m and as the La Liga window closes on September 2, United fear Real will wait in a bid to push through a cut-price deal.
But now the Mirror claim United will not sell the Frenchman at any price if Madrid try to poach him after the English deadline closes.
United have already warned they will raise their valuation of Pogba to closer to £180m if the French star and his agent Mino Raiola continue to agitate for a move.
It was thought that United would demand £150m for Pogba if they relent over his wish to leave Old Trafford for the second time in his career.
But after Pogba and Raiola both publicly indicated his intention to go this summer amid interest from Real Madrid and Juventus, United are ready to dig in and ramp up the price.
The United hierarchy have no wish to sell Pogba, who has up to three years left on his contract, and will make it as difficult as possible for him to leave.
But if they are forced to sell their record signing, the club are determined to get the best price possible.
A £180m fee would mean United double their money on a player who cost £89m from Juventus three years ago.