Sterling's future has been cast in doubt after he rejected a new contract at Anfield, and then said he was flattered to be linked with clubs such as Arsenal.
Real and Bayern Munich are among the clubs linked with a move for the 20-year-old, and Real legend Zidane - now in charge of the Spanish giants' B team and widely expected to be Carlo Ancelotti's long-term successor in the main job - has revealed the European champions are keeping tabs on Sterling.
"We know who Raheem Sterling is, and of course we are monitoring him as a player," Zidane told 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 [Gareth] Bale for over a year, the same with Isco and also [Raphael] 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."
