The Red Devils want £150million for the World Cup winner but it is claimed Los Blancos are preparing a £135m bid.
Pogba has been criticised for his inconsistent performances at Old Trafford and could be allowed to leave.
Ole Gunnar Solskjaer is conducting an overhaul of his squad and just completed the £15m signing of Daniel James from Swansea.
And in order to sign Pogba, Real Madrid are trying to sell 10 players to find a raid for the France international.
The Daily Star claim Gareth Bale, James Rodriguez, Dani Ceballos, Mateo Kovacic, Lucas Vazquez, Borja Mayoral, Martin Odegaard, Raul de Thomas, Marco Asensio and Isco could all leave the club.
There have so far been no offers for Wales international Bale although links to Manchester United persist.
Napoli are interested in Rodriguez while Kovacic could complete a permanent move to Chelsea if their transfer ban is frozen.
Tottenham and West Ham want Ceballos, Real Sociedad are eyeing Mayoral and Ajax and Bayer Leverkusen are interested in signing Odegaard.
Vazquez is also surplus to requirements at the Bernabeu as Zinedine Zidane looks to overhaul his squad.
And the reports claim Real could even listen to offers of Isco, Asensio and De Thomas.
Pogba has opened up on his relationship with United boss Solskjaer in recent days.
“People call him baby-faced but now he’s just a happy person,” Pogba told The Times.
“He smiles all the time and brings smiles to people. He’s really nice.
“I had the chance to be with him a few times in the reserves so I know him for a long time and I have a very good relationship with him.
“Once when I was at Juventus we saw each other. He’s a very nice guy and a very good person.
“He’s really nice with the players and very close with the players as well.”
United will find out their Premier League fixtures tomorrow morning at 9am.
The Red Devils are also looking to overhaul their squad this summer and have been linked with the likes of Bruno Fernandes, Aaron Wan-Bissaka and Matthijs de Ligt.