The 22-year-old joined the capital club from Villarreal last summer but could depart the club after just one season, according to Onda Cero.
The Spanish outlet says that although the midfielder has a contract until 2023 with Atleti, the club could not stand in his way if City match his €70 million (around £60 million) release clause.
Pep Guardiola’s side are said to be ready to fork out that sum to secure the Spain international, who has scored two goals in 26 La Liga appearances this season.
Rodrigo’s team-mates Saul Niguez and Thomas Partey have also been linked with a move to the Etihad, as the reigning English champions cast an eye to their summer transfer activity.
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