And it is claimed the midfielder is desperate to quit Old Trafford and move to the Bernabeu.
Pogba remains United’s record signing after rejoining the club from Juventus in an £89million deal in 2016 – four years after leaving for the Italian giants on a free transfer.
Now, The Mail claim agent Mino Raiola has already opened talks with Real and that Pogba himself has told friends he wants out of the club.
Pogba was unsettled before Jose Mourinho was sacked in December after a number of public fall-outs with his former manager.
He enjoyed a dramatic upturn in form following the temporary appointment of Ole Gunnar Solskjaer but has struggled badly since the Norwegian was named as Mourinho’s permanent successor in March.
Despite his worrying recent displays, Real Madrid boss Zinedine Zidane is a keen admirer of his fellow Frenchman and has made no secret of his desire to sign him.
It is also claimed United would prefer to keep their star man but they are reportedly open to offers of £160m or more.
That is unlikely to put Real off as Zidane is planning a summer overhaul of his squad after a dreadful season by their own high standards.
Zidane became their third manager in less than nine months when he returned for a second spell in the dugout at the beginning of March.
They are set to finish third in La Liga and were dumped out of the Champions League by Ajax in the quarter-finals.
Now, Real fans can expect to see a number of new faces arrive in the summer as Zidane attempts to turn their fortunes around.
Eden Hazard looks set to finally move from Chelsea after it was claimed Real will announce his capture once the Blues have finished their season.
The Spanish giants are also keen to bring in a new striker and Eintracht Frankfurt sensation Luka Jovic is said to be top of their list of targets.
Tottenham star Christian Eriksen is another reported target and he is about to enter the final year of his contract at the Tottenham Hotspur Stadium.
Real were hoping to take him in the summer as well but they could wait for his contract to run out and sign him in a free in 2020.