The Sun says the French World Cup winner is desperate to quit Old Trafford after giving up on their future league title chances.
It is understood the Red Devils are looking for a package of more than £160m for the 26-year-old.
Madrid have been looking to land him for the past three transfer windows now, and are still very keen.
The four are all up-for-grabs at the Bernabeu, with Zinedine Zidane allowing them to move on.
It is understood the last contact the two clubs had over Pogba and other transfer dealings was just last week.