The 20-year-old attacker has been a key man at Anfield for much of the last 18 months, playing a big role as the Reds came close to winning the Premier League title last year.
However, with his deal due to expire at the end of next season, Sterling’s future is in doubt after he spurned the club’s latest offer of fresh terms.
And despite his now influential role at Liverpool, Real are hopeful that the situation may allow them to land the Jamaican-born England international for as little as £26m next summer.
Such a sum would be below his market value, which was recently estimated at around £36.6m.
However, Brendan Rodgers has insisted that he expects a deal for his youngster to go through, having described him as “very happy” on Merseyside.