The left back joined Real in 2011 from Sporting's rivals Benfica for a reported fee of 30 million euros ($33.37 million)to provide competition for Brazilian Marcelo.
Persistent injuries, however, hampered his progress in Spain.
Coentrao has played 106 games in five full seasons for Real, spending the 2015-16 campaign on loan at Monaco. He has never played more than 20 league games in a single season. In that time he has won two La Liga titles, two Champions Leagues and a King's Cup.
Coentrao has made 51 appearances for Portugal although a thigh injury prevented him from taking part in his country's victorious Euro 2016 campaign.
Following his injury ravaged season at Monaco, where he played 15 league games, Coentrao returned to Madrid last summer.
He made six appearances in all competitions last season, and was left out of the squad for the Champions League final victory over Juventus.
(Reporting by Richard Martin; Editing by Toby Davis)
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