The 36-year-old is yet to extend his contract with Los Blancos beyond 2022, although there is thought to be confidence from both sides that an agreement can be reached.
However, with Modric now in the final six months of his deal with Carlo Ancelotti's side, the 2018 Ballon d'Or winner is free to enter talks with foreign clubs.
According to El Nacional, Man City are keeping a close eye on Modric's situation, with the Croatia international now 'running out of patience' over contract talks.
The report adds that Modric wants to hang up his boots at Madrid and is willing to take a hit on his salary to stay until 2024, but Pep Guardiola's side will swoop if talks fail to bear fruit.
The former Tottenham Hotspur man has five assists from 20 appearances in all competitions this season and has won four Champions Leagues and two La Liga titles at the Santiago Bernabeu.