Sterling recently refused to sign a new 100,000 pound-per-week contract, but insists that despite this he is not a "money-grabbing 20-year old".
As Sterling has not committed his future to Anfield, Zidane, who coaches Real Madrid Castilla, the club's 'B' team, insists that Los Blancos are interested in signing him.
"We know who Raheem Sterling is, and of course we are monitoring him as a player," Zidane, who is reportedly set to replace Carlo Ancelotti as Real Madrid's head coach, was quoted as saying by the Daily Mail.
"There are very few players in the world who can improve the Real Madrid squad, so it is going to make sense we monitor the progress of the best young players in the world.
"We monitored Bale for over a year, the same with Isco and also Varane.
"We monitor many of the best young players in Europe, then if we feel they have something to offer Real Madrid we will contact their club and try and make the next step."