The 26-year-old has been one of City's standout players so far this season, scoring four goals and creating nine more across all competitions to help them into a commanding eight-point lead at the top of the Premier League table.
Spanish news outlet Don Balon claims that De Bruyne's form has captured the attention of Real Madrid, who are now considering a move for the Belgium international.
Madrid president Florentino Perez is looking at a number of high-profile targets in an attempt to improve his side's fortunes having seen them slip 10 points behind Barcelona after just 12 games of the season.
Los Blancos are reportedly willing to spend up to €100m (£88.6m) on the playmaker, who joined City for a reported £55m in 2015.
However, City boss Pep Guardiola is unwilling to sell one of his prized assets and remains hopeful that De Bruyne will sign a new deal at the Etihad Stadium instead.