Los Blancos are believed to be keen to lure Rodri back to his homeland after he previously played for Real Madrid's local rivals Atletico Madrid.
Despite their interest in Rodri, Real Madrid opted to boycott the recent Ballon d'Or awards after the Man City star pipped Vinicius Junior to the top prize.
Rodri previously stated that he was not bothered by Real Madrid's non-attendance, although he admitted it was a stance he would not have taken.
"All the Spanish clubs would have to congratulate me and they haven't," Rodri told Cadena Cope. ""I care about my family and my club. They must have their reasons; I wouldn't have done it that way and there's no point in going over it.
"The mistake is giving so much attention to a club that hasn't decided to participate."
Rodri opens door to Real Madrid switch
Real Madrid's reaction to Rodri Ballon d'Or triumph has not stopped them from being linked with a potential move for the Spain international.
Rodri has opened the door to the prospect that he could join Real Madrid in the future, conceding that he would have to listen if a potential offer was put on the table.
The 28-year-old told El Larguero: "When Real Madrid call you, the best club in history and the most successful... it makes you proud and you always have to listen. It's obvious. You always have to pay attention."
While Rodri may be open to a future move to the Santiago Bernabeu, it would take a significant offer for Man City to part ways with the Euro 2024 winner.
The Premier League champions would be in a relatively strong negotiating position, with the midfielder under contract until the summer of 2027.
Why do Real Madrid want to sign Rodri?
Undoubtedly, any major European club would love to have Rodri's services, with the Spaniard widely regarded as the best midfielder in the world.
Rodri remains one of Man City's key players despite being sidelined for a significant period with an anterior cruciate ligament injury.
As a result, the Citizens will be reluctant to sanction his departure, but Real Madrid may be one of the clubs that have the pulling power to prise Rodri away from the Etihad Stadium.
Having spent the last five years in the Premier League, Rodri may also be keen to return to his homeland while he is still in his peak years.
Real Madrid likely view Rodri as the perfect candidate to fill the void left by Toni Kroos, who retired from professional football in the summer.