Coentrao came close to joining United in a loan deal on deadline day, but the deal fell through in the last few minutes of the window.
The deal fell through as Real Madrid failed to bring in a replacement for Coentrao in time.
United boss David Moyes is keen to bring in competition for Patrice Evra at the left-back, according to Metro.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?