The Spanish club believes Rodri is the ideal player to replace Toni Kroos, who retired last summer.
Many within Real Madrid feel that they have not adequately filled the void left by Kroos' departure.
Rodri, the reigning Ballon d'Or winner, is recovering from ACL surgery he underwent in August.
Manchester City might be hesitant to sell Rodri in the summer, as he has expressed a desire to play in La Liga before the end of his career.
