However, the Champions League winners face competition from Chelsea, who are also keeping tabs on the 27-year-old.
Sterling, who represents himself, has one year remaining on his current contract but is yet to agree on terms for a fresh deal.
Real Madrid and Chelsea Monitoring England International
Real Madrid Looking to Add
Following their La Liga and Champions League triumph, Spanish giants Real Madrid aren’t resting on their laurels.
Having seen the departure of Gareth Bale, the injury proneness of Eden Hazard and the uncertain future of Isco, Raheem Sterling would be a useful addition to an already potent attack.
Sterling can operate on either flank but has also played in the number nine role for Manchester City in the past few seasons given their lack of a centre forward, and his goals and assists tally prove what an asset he would be.
Should Sterling look to leave City but remain in the Premier League, Chelsea have also expressed interest in the England international.
The future of Romelu Lukaku is unclear, despite only arriving last summer, while the inconsistent form and lack of game time for Timo Werner, Callum Hudson-Odoi and Hakim Ziyech pinpoint a new arrival could be crucial for the Blues.
England International at Manchester City
There is no doubting the qualities of Raheem Sterling. The 27-year-old joined Manchester City in 2015 and is closing in on 350 appearances for the club.
During that time, he has scored 131 times and added 95 assists. He has also won four Premier League titles, one FA Cup and three League Cups.
However, with the club looking to add two more players this summer following the arrival of Erling Haaland, game time at the Etihad could be limited, particularly as he has played fewer minutes over the last two seasons.