Much was expected of the Dutchman after his £25million summer move from PSV, but he has failed to live up to expectations.
His struggles have seen him drop to the bench, with Anthony Martial preferred on the left-wing in recent weeks.
However, The Telegraph claim Real have seen enough to suggest he is far from a lost cause just yet and could be prepared to offer him a lifeline.
The 21-year-old's woes were further compounded this week when he was dropped from the Holland national team squad.
Manager Danny Blind has accused him of being selfish and said: "I think Depay is a player for the future.
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Memphis Depay has struggled to settle into life at Manchester United
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Depay has also been dropped from the Holland national team
"But there are other issues to look at. Perhaps Louis van Gaal has also said something.
"In football you must function in a team. He doesn’t always do that.
"I have also told him when I called him to say he’s not in there. That’s something he has to learn."
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