The left-sided Portugal international has been linked with the Red Devils, Real and Barcelona but admits his preferred destination would be the Bernabeu.
Coentrao, 23, said: "I know that Manchester United and Barcelona are interested in me. This is special for me and makes me think that I am doing well as a player. They are two big teams with the best players but if Real Madrid show an interest they will be my first option.
"There is a mutual interest between me and Real Madrid. However, it is up to the clubs to reach an agreement over a transfer fee. I can only hope that my dream of playing for Real Madrid will become reality."
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