According to Spanish outlet Diario Gol, Real president Florentino Perez is desperate to sign the France international.
But it is said that Pogba has his mind already made up and he wants to join Lionel Messi at Barcelona.
The Catalan club are running away with the league title and are through to the Champions League quarter-finals.
Diario Gol add that Pogba has told his closest friends of his wish to play alongside Messi, who many people consider to be the best player of all time.
GETTY
Pogba reportedly wants to play alongside Lionel Messi.
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But United boss Jose Mourinho will be desperate to keep hold of his £89million man as he too plans to strengthen at the end of the season.
The Portuguese boss dropped the midfielder for a number of games in February after a string of poor performances.
And that has led to speculation that Pogba could soon depart Old Trafford.