The Dutchman was sold to French side Lyon in January for £15million as Jose Mourinho tried to rid the deadwood from his side.
The fee was £10m less than what the Red Devils paid PSV Eindhoven for his services just two years prior.
The 23-year-old failed to live up to his reputation when he arrived at Old Trafford.
Depay scored just seven goals in 53 appearances as he failed to make the grade.
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Memphis Depay says he will play for Real Madrid
I think I'm going to Real Madrid. Yes, that's a serious goal.
Memphis Depay speaking about his next career move
And since his move to France, he has netted seven goals in 25 games at the Groupama Stadium, and he now thinks his performances have warranted a move to La Liga giants Real.
"I think I'm going to Real Madrid. Yes, that's a serious goal." he told The PSV Supporter magazine.
"What's happened so far, that's God, he helps me and brings me here.
"I had very nice times at PSV, but I wanted to reach higher goals in my career. At Lyon I'm very happy. The club is in a way comparable to PSV."
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Memphis Depay scored seven goals in 53 appearances for Manchester United
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Paul Pogba was allowed to walk for free before returning for £89million
If Depay gets his dream move to the Bernabeu it would be another blow to United's recruitment policy.
Mourinho's side have been stung before by letting players go on the cheap before going on to greater heights.
Midfielder Paul Pogba is the prime example, being allowed to join Juventus on a free transfer before being bought back for £89m.
