Rodri, who has shone in his debut season at Atletico, has a £61.2million release clause and could follow Antoine Griezmann out of the door after the Frenchman announced he would be leaving the club this summer.
With Diego Godin and Juanfran set to leave, too, Atletico boss Diego Simeone will be reluctant to lose Rodri.
But Spanish outlet AS say the 22-year-old is ‘very near’ to agreeing a deal to move to the Etihad Stadium and is attracted by the prospect of playing under Pep Guardiola.
Rodri, a defensive midfielder, has been compared to Barcelona ace Sergio Busquets.
Atletico president Enrique Cerezo hinted the club would not block a potential exit for Rodri if the right offer was made and the player wanted to leave.