The France international is out of contract at Old Trafford in the summer and as yet has shown no sign of wanting to extend his stay.
Pogba trained for the first time in two and a half months on Monday following a thigh injury, and is set to play again early next month.
The Daily Star says by then, United's record £89million signing will have less than five months left on his £295,000-a-week contract, and he wants to link up with LaLiga leaders Real Madrid once his deal is up.
The report claims the midfielder - who joined from Juventus in 2016 - held talks with senior club figures several weeks ago in which he disclosed his intentions to move to Spain.
United meanwhile have reportedly not offered Pogba a new deal and are now willing to let him depart on a free transfer.
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