Liverpool would dearly like to keep the German international midfielder at Anfield but that is looking increasingly unlikely as he is out of contract next summer and free to discuss his future with any new clubs in January.
Los Blancos are the latest big club to take notice but they will ace some stiff competition with Italian giants Juventus the favourites to land the player.
With both clubs now in the hunt it could well be that Liverpool decide to cash in in January and sell to the highest bidder, rather than let him leave for nothing next summer as he is showing no signs of putting pen to paper over a new deal.
Meanwhile, Dani Ceballos is set to spark a scramble for his signature by pushing for a move away from Madrid in the January transfer window.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.