Sterling has enjoyed an excellent year of form, securing his status as a key player for both club and country after becoming a regular in the Liverpool team in the early stages of last season.
According to The Mirror, his rise to prominence has been followed closely by Ancelotti, who is eager to bring the 19-year-old to the Spanish capital in the next summer transfer window.
Although Madrid have never made contact with Liverpool about Sterling, the report claims that the delay over a new contract for the attacking midfielder has alerted the Champions League winners to the possibility of securing a deal.
Liverpool boss Brendan Rodgers recently revealed that he was reluctant to give a player in Sterling's position a lucrative contract at such a young age.
Sterling's current deal expires in 2017.