The Brazil international's future at Real remains clouded after falling out with former coach Carlo Ancelotti towards the end of last season.
The Italian's successor, Xabi Alonso, has been bullish about keeping hold of the attacker for the new season, but he is still unhappy with his drop in status over the past 12 months.
OkDiario's chief pundit Eduardo Inda, when speaking on El Chiringuito, revealed contact is being maintained between Rodrygo and City.
He said: "I think Rodrygo could be the great outing this summer. We will wait until the end of the Club World Cup to see it. The club has put a price on him. It is the team that has always loved him, although half of Europe loves him. Real Madrid has valued the player at 100 million euros.
"They could go down to 80 or 85 and pay the rest in easy installments. Not only City has been interested. Rodrygo has also received a traditional offer from Saudi Arabia."