The Portuguese international left-back has been linked with a moved to Old Trafford in recent years.
He indeed agreed a move to the then David Moyes' side on transfer deadline in summer 2013 but the deal collapsed at the last minute when Los Blancos failed to secure the services of current Atletico Madrid star Guillerme Siqueira as his replacement.
Louis van Gaal also reportedly had him on his shopping list last summer before opting instead to sign Luke Shaw, while earlier in March Coentrao himself reignited speculations over a potential move to United amid reports claiming the Premier League giants will try his signing once again at the end of the season.
"I already showed that interest in playing there [at Manchester United]. It's one of the best clubs in the world, a club that I admire a lot. It would be an honour to play there," Coentrao said in March.
Marca report Real Madrid want to include him in the negotiations to secure a cut-price deal for De Gea after the left-back has fallen out of favour with Carlo Ancelotti during the current campaign – starting just five La Liga games.
The Champions League winners have reportedly already agreed personal terms with the keeper and now just need to reach a fee with United to complete the signing of the keeper.
The Spanish newspaper claim Real Madrid have tabled a first bid in the region of €20m, but van Gaal's side are reportedly demanding €40m (£28.7m, $44.7m) for the keeper.
So Marca claims that the inclusion of Coentrao, who was signed by Real Madrid in summer 2011 for £27m, could be the key to reach a cut-price agreement which satisfies all the parties.