The Daily Mail says United tried and failed to take on loan at the end of the summer transfer window in August.
Although that deal fell through, the player has subsequently endured a tough time, suffering a hamstring injury while with his national side. He also lost his father in November.
Coentrao is eager to make a fresh start and a move to England and Old Trafford appeals.
It is expected United would have to come up with about half of the £25million Real paid Benfica for the 25-year-old in the summer of 2011.
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