The 22-year-old Uruguayan joined Real Madrid from Penarol in 2016 and has been slowly progressing into the first team since then.
The central midfielder made 44 appearances in all competitions last season and has played in all five La Liga games so far this campaign, starting three of them.
Real Madrid value him highly, illustrated by the absolutely mammoth release clause in his contract of £640m, but United believe he could be brought in if Pogba finally does make his long-expected move to the Spanish capital, reports the Sun.
Pogba has openly admitted that he wants to move to Real Madrid, while Real boss Zinedine Zidane has made no secret of his interest in signing his countryman.
The French midfielder has had his Manchester United contract extended by an extra year, with it now running until 2022, but he could still be sold next summer.
As recently as last week Pogba admitted that he fancied the idea of playing for the La Liga champions, saying: ‘Yes, all footballers would like to play for Real Madrid.
‘Maybe it is a dream. It is a dream for me, why not one day? As I have said, I am at Manchester United and I like my club.
‘I am going to give my maximum, like my teammates. I prefer to concentrate on football and on returning to fitness.’
Man Utd boss Ole Gunnar Solskjaer is adamant that Pogba will be staying for two seasons, though, and has talked up what he expects from the World Cup winner in that time.
‘Paul’s our player, he’s going to be here for another two years and sure he’s focused on doing his best for us and we want to see the best from Paul and I’m sure in the next couple of years we’ll get the best out of him,’ said the Red Devils boss.