United have had scouts watching the Gremio youngster and Marca claim Real have been watching him for more than 12 months.
“He is a player we like and does seem to be very interesting,” United boss Sir Alex Ferguson is quoted by Spanish daily Marca.
“He [Douglas] is a player that will soon be in Europe,” Manchester United forward Anderson told Globosport.
“But he has to win a title before joining a big club in Europe.”
He added: “Lucas told me there was this good boy emerging.
“But people have to be calm, he is an above average player and you have to give him confidence.
“Everybody needs support and he needs to be able to play.
“He will probably soon be past me, past Ronaldinho and everyone.”