Super Deporte says City made an offer of €20m rising to €35m during the close season transfer window.
However, Los Che owner Peter Lim held his nerve and resisted the City money.
City's scouts clearly were on their game with Rodrigo kicking off this season in superb form. So far this term, the striker has four goals in seven games and also provided two assists.
The 26 year-old has past experience in England with Bolton Wanderers.