The teen prodigy has been linked to Los Blancos after impressing for England against Italy.
At this stage it should be viewed as merely a rumour given the nature of the source, low figure and non-committal timing, but even so, such news raises the interesting question regarding Sterling's future should he continue his ascent to superstardom.
The better he performs for club and country the more his name will be linked to the likes of Madrid but whether a move away from Anfield in the immediate to short-term would be wise is far less certain.
The 19-year-old needs to continue his footballing development at Liverpool and there is not a better manager around at present than Brendan Rodgers for him to learn his trade under.
At Madrid Sterling would most likely see much less game time given the array of talent in the squad and that could well stunt his progress.
The Champions League winners already have the talented Jesse waiting in the wings and if long touted academy product Alvaro Morata cannot make it at the Bernabeu then what chance the Jamaican born attacker?
There is a feeling that Real president Florentino Perez would buy Sterling now just to say he plays for Madrid and no one else. After all Perez has used that policy for many a player before and seen their careers ultimately unfulfilled.
Sterling has time on his side so any big move can always wait further down the line should he be so inclined.
Gareth Bale joined Real at the age of 24 and perhaps at that age the former QPR youth product could make stake a regular place in the starting line-up of quite possibly the world's biggest club.
As it is Sterling should carry on keeping his down and improve his game, most notably his goalscoring. While he has taken note of Rodgers' insistence that he get into the box more frequently, his finishing still needs further work but that will no doubt come with time.
In the meantime Liverpool have a truly frightening prospect on their hands for the next few years if not more