Madrid have been monitoring Sterling for some time and may be ready to make a move for the youngster, the Daily Mail reports.
Sterling is currently said to be earning £30,000 a week with three years left to run on his current deal, though Reds manager Brendan Rodgers has recognised the importance of keeping the England international at Anfield.
"This kid is only going to get better," Rodgers is quoted as saying.
"He's way above the level from when he first came in. In big games he's performed and he's a wonderful talent."
Sterling, 19, joined Liverpool from Queens Park Rangers in 2010 for a fee of £600,000, rising to £5m depending on first-team appearances.