The 26-year-old has reportedly already agreed personal terms with the LaLiga giants and has asked to leave Old Trafford.
Pogba’s Manchester United future has been thrown into doubt this season as the midfielder admitted a move to Real would be a ‘dream’.
United are sixth in the Premier League, with Sunday’s draw with Chelsea keeping them three points off a Champions League spot with two games to go.
Ole Gunnar Solskjaer’s men have won just one of their past four league games with Pogba’s form dropping off throughout that period.
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The France international has not scored from open play since February.
Failure to secure Champions League football could lead to his departure from Man United at the end of the season.
Spanish outlet AS claim United players have been joking with Pogba about a potential move to Real.
One unnamed player is alleged to have said ‘If you go to Real, do not forget me’ and ‘Invite me when you’re playing at the Bernabeu’.