Manchester United and Michael Carrick are keen to bring the 26-year-old midfielder to Old Trafford, who is worth an estimated £68 million, per Samuel Luckhurst of The Sun.
The Red Devils have already brought in Andrey Santos and Youri Tielemans during the summer transfer window, and they now want to sign a more defensive-minded midfielder.
Real on the other hand are desperate to sign World Cup 2026 winner Rodri, who was named the best player of the tournament after Spain's victory over Argentina in the final.
The 30-year-old has 12 months left on his contract at Manchester City, and is set to undergo minor surgery which will see him miss the start of the new Premier League season.
Rodri is valued at £85 million pounds by City.
Jose Mourinho is adamant that he want to bring in the La Roja skipper, and although he had initially planned to keep Tchouameni, his hand may be forced to sell the Frenchman to get a potential deal for Rodri over the line this summer.