Both of the Premier League sides were linked with moves for the Portuguese international over the summer, but it was the Red Devils who came closest to sealing a loan deal for his signature only to see their efforts thwarted by a failure to process the switch before the deadline passed.
Despite failing to lure him to England last time around, the duo are still keen to snap up Coentrao in the New Year.
The 25-year-old has spent much of the current campaign warming the bench at the Bernabeu, with new Real boss Carlo Ancelotti having made Marcelo his first choice left-back.
As a result, the former Benfica man is believed to be ready make a move in a bid to keep his hopes of featuring in the 2014 World Cup – for which his nation must overcome Sweden in a play-off clash – alive.
United may make a fresh move with the future of Patrice Evra unclear, while Tottenham manager Andre Villas-Boas is keen to bolster his defensive options with an injury to his only orthodox left-back, Danny Rose, having forced Jan Vertonghen to fill the void.
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