The 25-year-old Coentrao joined Madrid in 2011 from Benfica and he has impressed, playing at both full-back and in midfield.
However, with Mourinho's departure confirmed and the Portuguese coach expected to join Chelsea, Coentrao is looking to follow his fellow countryman through the Bernabeu exit doors.
Speaking to Ojogo in his homeland, Coentrao said: "From the first day I do not think I was wanted here.
"Today it seems that everyone wants me to leave the club. I do not know what I have done wrong.
"We must find a solution that is good for both the club and myself, so that no one will lose out."
Coentrao was asked about the prospect of following Mourinho to Chelsea, and he admitted he would not rule it out.
"If I leave Real Madrid, I do not close the door to anyone," he said.