Pogba, 28, started the season in superb form and has played a starring role for the Red Devils after reportedly being impressed with Ole Gunnar Solskjaer's summer recruitment.
But he has yet to agree a new deal and Catalan publication El Nacional claim agent Mino Raiola has offered Los Blancos the chance to sign the superstar playmaker.
Real currently sit top of LaLiga after an unbeaten start and are hot on the heels of Paris Saint-Germain sensation Kylian Mbappe, who is also out of contract this summer.
Jose Mourinho wants to bring Tottenham misfit Tanguy Ndombele to Roma after working with him at Spurs, claim CalcioMercato
Tottenham are plotting a swoop for West Brom and England goalkeeper Sam Johnstone, according to a report in The Sun.
Italian outlet Fichajes suggest United flop Donny van de Beek could be offered an escape route by AC Milan.
Manchester City want Villarreal star Pau Torres to add another option at centre-back, claim Marca.
FC Salzburg hotshot Karim Adeyemi is at the centre of a transfer battle between Liverpool, Bayern Munich, RB Leipzig and Wolfsburg, according to Sport Bild