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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.