The Spanish giants have been searching for a long-term successor to midfield legends Toni Kroos and Luka Modric, and Rodri is believed to be their preferred choice.
According to reports from The Athletic, Real Madrid are working behind the scenes on a deal for the 30-year-old, although formal negotiations with Manchester City have not yet begun.
Rodri has just one year remaining on his current contract, leaving City with a decision to make. If the midfielder does not agree to a new deal, this transfer window could be the club's last chance to receive a transfer fee for one of their most influential players.
Despite that, City are determined to keep hold of the World Cup-winning midfielder, who played a key role in Spain's triumph at the 2026 FIFA World Cup.
If the move goes ahead, Rodri would become the latest high-profile departure from the Premier League club following the exits of Pep Guardiola, John Stones and Bernardo Silva, with Silva also making the switch to Real Madrid.
City manager Enzo Maresca has dismissed the growing speculation and insisted Rodri remains part of his plans.
The midfielder is due to undergo minor back surgery next week after captaining Spain to World Cup glory, and Maresca said his immediate focus is on Rodri's recovery rather than transfer rumours.
"We have to say that around big players there are always speculation," Maresca said.
"I'm not worried about that, it's normal. They won the World Cup and he was one of the best players.
"Every manager wants to have Rodri, but now surgery. He needs to rest and recover, and then he will be back here with us."
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Chelsea manager Xabi Alonso believes new signing Morgan Rogers has everything needed to make an immediate impact at Stamford Bridge and says the England international will strengthen the club's attacking options.
Real Madrid have reportedly moved a step closer to securing one of Europe's brightest young talents after agreeing personal terms with RB Leipzig winger Yan Diomande.
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