According to Mundo Deportivo, the 28-year-old is rumoured to be on the radar of the Spanish champions.
The Portugal international been impressive for City so far this season, scoring two goals and providing five assists in 26 appearances.
However, City head coach Pep Guardiola limited use of Cancelo since the season restarted last month has sparked interest from the European champions.
Real Madrid are considering adding a new right-back to their squad during the summer transfer window, and Cancelo has been identified as a possible acquisition.
It remains to be seen whether the Portuguese will leave Manchester City in light of Real Madrid’s interest.
Cancelo will see his contract at the Etihad Stadium expire at the end of 2026-27 season.