The Spanish giants have endured a difficult season since Cristiano Ronaldo left for Juventus, falling to sixth in the Liga table and replacing manager Julen Lopetegui with Santiago Solari.
And now The Sun claim Real president Florentino Perez is prepared to spend big to get Real firing again and wants both Rashford and Eriksen to fill the void left by Ronaldo.
Real sent scouts to Wembley on Sunday to watch Rashford and were impressed by his performance against Croatia.
New boss Solari is a big fan of Rashford and the club believe he could replicate Ronaldos transformation after leaving Old Trafford for the Bernabeu.
Real are hoping to land Rashford for a rather optimistic £50million, while they see Eriksen as a long-term successor to the 33-year-old Luka Modric.
The Dane is stalling on signing a new deal with Spurs and will be out of contract in 18 months, with Real hoping they might be able to prise him away for as little as £40m.
Madrid have had a number of scouts at Old Trafford recently and many at the club feared it was Paul Pogba they were looking at, though it was actually Rashford who caught their attention.
They are not the only European giant who have been impressed with the England man, with Italian champions Juventus also keeping tabs on him.
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