He played a blinder against United in the Champions League and attracted the interest of Alex Ferguson.
He said: "Of course I would love to play for Manchester United. They are a great team and it is a dream for anyone to play in great clubs."
Spanish giants Real also want versatile midfielder Veloso, 21, who can play in defence as well.
Sporting president Felipe Soares Franco admits Veloso is a major target but will put up a fight to keep him.
Franco said: "There is no chance the player will leave. We are not interested in negotiating this subject because Miguel Veloso is one of our main players for this campaign."