The Daily Star says the Spanish giants have made the Old Trafford ace their No.1 summer target.
United plan to open new contract talks with Rooney next month about a possible £170,000-a-week deal.
But Madrid hope to turn Rooney's head and intend to pursue the England striker in the same way they trailed wing wizard Cristiano Ronaldo last season.
Madrid eventually landed Ronaldo for £80m and United fear they will make an offer for Rooney that they will struggle to turn down. Real president Florentino Perez wants to maintain the second coming of the Galacticos and add Rooney to Ronaldo, Kaka and Xabi Alonso.
A Madrid source revealed this week: “Rooney is the top name on the list for next summer. Madrid will pursue him in the same way they did with David Beckham and Ronaldo. They are always successful and will do what it takes to get Rooney.’’