The Spanish side are ready to make a move next summer as coach Jose Mourinho has ruled out making any signings in the january transfer window.
The Daily Star reports that Real have made Rooney their main £75million summer target.
Madrid sources said last night told The Daily Star: “There is no haste in the subject. It is something which can be completed at the end of the season.
“We know Rooney has not signed a new deal. Real are ready for the battle with Alex Ferguson. They know what to expect, they have been down this road before.”