Benzema's future at the Bernabeu has been cast into doubt so far this term, with the 29-year-old having scored only two La Liga goals all season as Madrid have fallen 11 points adrift of leaders Barcelona.
Arsenal and Paris Saint-Germain are understood to be monitoring Benzema's situation at the Bernabeu with a view to a possible move, although any deal would rely on Madrid bringing in a replacement first.
Spanish news outlet Don Balon reports that Man City have now joined the race, with manager Pep Guardiola understood to be a long-term admirer of the France international.
City already have the likes of Sergio Aguero and Gabriel Jesus at their disposal, but Guardiola is keen to add even more attacking firepower to his squad, with Alexis Sanchez also being linked with a move to the Etihad Stadium.
Benzema only signed a new contract with Madrid in September, but club president Florentino Perez is expected to splash the cash in January in an attempt to salvage their season.