The 19-year-old winger emerged as one of Premier League’s top performers over the latter half of last season, with his mature performances almost guiding the Reds to a first league title in 24 years.
Since then the youngster has been involved in the England squad at the World Cup, where he has been one of the few shining lights in a campaign which sees the Three Lions’ dreams in tatters before Group D has even reached its climax.
This has alerted Real, who are considering replacements for Angel Di Maria.
The Champions League winners have already been linked with Suarez, and now they want to complete an astonishing double swoop for the attacking pair.
Although a wide-man, Sterling has shone in a central role just behind the main striker, and is considered to be one of the world’s very best emerging players.
English stars have rarely shone abroad, but Real have shown a willingness to snap up players from the country with David Beckham and Michael Owen two examples.
Liverpool are unlikely to consider letting Sterling leave, with reports having suggested that he’ll be rewarded with a bumper contract for his performances by the club.