Having lost Dani Carvajal to a knee injury and Lucas Vazquez struggling with his fitness, Real Madrid were in the market for a new right-back midseason.
The Athletic says City made contact with Real Madrid about taking on club captain Walker, 34.
However, City did not receive any type of feedback, not even a courtesy 'thanks, but no thanks', from the Spanish giants.
Walker eventually went onto join AC Milan to the end of the season.