City have been hit with a two-year European suspension after being found guilty of "serious breaches" in relation to Financial Fair Play regulations.
As it stands, the Premier League champions will not be able to play Champions League football until the 2022-23 campaign, which could allegedly see a number of players leave the Etihad Stadium.
According to The Sun, Madrid are preparing to 'launch an all-out assault' to land Sterling in an £180m deal during this summer's transfer window.
The 25-year-old has a contract at the Etihad Stadium until the summer of 2023, although it is thought that talks over a new and improved deal started in November.
The England international has scored 20 times in 35 appearances for Pep Guardiola's side this season, including five in six outings in the Champions League.