Don Balon says Real president Florentino Perez has set his sights on Sanchez.
The centre-back impressed against Real in the Champions League this term.
And Real are keen to get him on-board having previously had him on trial, but they are not going to make an imminent move for Sanchez.
Last week, the Colombian said: "Right now, here in Tottenham I am very good. I am playing every three to four days. I am being important in the team.
"As big as Madrid is, no matter how big a team are, that has won what they have won, if the conditions are not favourable for me, unfortunately I cannot accept."