The Brazilian has failed to make much of an impression in the Spanish capital since his 68 million euro ($89 million, £56 million) move from AC Milan in June 2009 in what was then a world transfer record.
It had been hoped that the appointment of his former boss at Milan, Carlo Ancelotti at the Bernabeu may have been able to inspire him to rekindle his old form, but the signing of Isco and the imminent arrival of Gareth Bale has instead seen him slip further down the pecking order.
“I want to leave,” he told reporters after scoring twice in Real’s 4-0 friendly win over Deportivo la Coruna on Thursday.
“I think it is the right moment for me and for the club to leave in an amicable fashion.
“I have spoken with Ancelotti and the club so everyone knows. My father (and agent) is speaking now with the club to try and resolve the situation.
“Things are now difficult for me to get into the team and the club know what I want.
“It is my obligation to work and continue training, but my father is already working to see if anything comes up.”
The 31-year-old has been an unused substitute in both Madrid’s first two La Liga matches and his desire to leave is even more immediate given that the World Cup will be played in his homeland next year.
He hasn’t been called up by Luis Felipe Scolari since March and missed out on the Confederations Cup success back in June.