According to Marco Ruiz of AS, the Frenchman is still keen to depart Old Trafford despite the exit of Jose Mourinho, and his agent, Mino Raiola, is already working on a transfer, with a return to Juventus also a potential option.
As Ruiz noted, Pogba, 26, was linked with Barcelona earlier this season amid tensions with Mourinho.
The Portuguese manager was replaced by Ole Gunnar Solskjaer back in December, though, and Pogba has flourished under the Norwegian:
Sky Sports Statto @SkySportsStatto
Paul Pogba scored his 11th goal of the season tonight - best goalscoring season of his career: 2018-19 Man Utd - 11 goals 🥇 2014-15 & 2015-16 Juventus - 10 goals 🥈 6 goals & 4 assists in PL since Ole Gunnar Solskjaer's 1st game on Dec 22 - most of any player 🔥🔥 https://t.co/tyL03Ol09M
But while on international duty with France, he said that Real is a "dream club":
Any club wanting to prise Pogba away from United will have to be prepared to make a huge bid, as the Manchester outfit will want to make a profit on the £89 million they paid to re-sign him from Juve in 2016.
Real are one of the few clubs in the world with the financial clout to even countenance signing the midfielder, and Juve showed they will splash the cash when necessary when they signed Cristiano Ronaldo for nearly £100 million last summer.
Pogba's current contract at Old Trafford runs to 2021, so United will be able to demand a big fee if the midfielder does indeed want out.
If he continues with the Red Devils into next season, though, the Manchester giants will need to push to sign him up to a new deal or else risk losing him relatively cheaply.
In an ideal world, United would surely be eager to keep Pogba for the long term, because he has shown under Solskjaer he could be the club's talisman for the best part of the next decade.
Qualifying for next season's UEFA Champions League could become a crucial factor in Pogba staying at Old Trafford, and United are in a fierce battle for the final two top-four spots in the Premier League.