The People says Coentrao is a target for Tottenham - regardless of his club's pursuit of Gareth Bale.
The 25-year-old's representatives expect to speak to Spurs officials today in a bid to move negotiations on.
Coentrao is a long-term favourite of White Hart Lane boss Andre Villas-Boas, who has already seen two bids to bring the player to England, first with Chelsea and then with Spurs, rejected by Real.
Coentrao has a release clause in his Madrid contract of £21.5million, but he is not part of new Real boss Carlo Ancelotti's plans and he will be offloaded for around £13m.
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