Madrid confirmed on Wednesday that long-serving defender Ramos will leave the Bernabeu at the end of the month.
Ramos has spent the past 16 years with Los Blancos, but the two parties could not agree terms on a new contract.
The 35-year-old is expected to have a number of clubs to choose from in terms of his next career move, though his salary could prove a sticking point for many.
According to AS, United and City are two teams in a position to match Ramos's salary demands, and the Premier League pair are both in contention to sign the Spaniard.
Among other major honours, the Camas native won five La Ligas, four Champions Leagues and two Copas del Rey during his time with Madrid.