The rumours have been simmering throughout this year's campaign about a possible move to the Bernabeu for the Polish striker and reports on Saturday have continued with this theme.
The aforementioned Catalan newspaper has claimed that Jose Angel Sanchez, Madrid's general director, has agreed to the signing with the player's agent Pini Zahavi, who was heavily involved in Neymar's transfer to Paris Saint-Germain.
Having decided to leave Bayern Munich, Lewandowski would join 'Los Blancos' for two seasons, with an option of a third depending on his performances, and would receive a salary far higher than he would get with the Bavarian club.
Although Zinedine Zidane has always protected his No. 9 Karim Benzema, the Frenchman has disappointed this season and the Madrid board are losing patience so could sell him to bring in a new face.
Tottenham's Harry Kane is their preferred target but the club have accepted that it will be an almost 'impossible' task to lure the Englishman from London this summer, so will settle for Lewandowski instead.