The proposal to hold a league game across the Atlantic stems from a 15-year partnership between La Liga and media company Relevent. Charlie Stillitano, the executive chairman of Relevent, remains positive about going ahead with the match despite widespread opposition.
"We are trying to be respectful to everyone involved," Stillitano insisted back in September.
Those against the fixture currently slated for Jan. 26, 2019 in Miami are perturbed by Girona - playing only their second season in La Liga - effectively losing a home match against their huge local rivals, thereby sacrificing the fair scheduling of Spain's top flight.
Real Madrid said in their letter to the RFEF that it's "fundamental" for teams to play "home and away at each other's stadium" for "the integrity and equality" of La Liga, as reported by BBC Sport.
The letter continued: "First of all we would like to declare that Real Madrid were never informed that La Liga had requested to play the game nor of the intention to make the request, and we were never asked our opinion on it.
"Nor, obviously, did La Liga obtain Real Madrid's agreement, despite the fact that this game affects a competition in which we participate."
The RFEF and the Spanish players' union (AFE) have previously voiced opposition to the proposal to play a match in the United States. La Liga and Relevent also need to seek approval from UEFA, the United States Soccer Federation, and CONCACAF, which is the governing body of football in North America, Central America, and the Caribbean.
After holding a meeting with La Liga last month, the AFE said the final decision on whether the U.S. match goes ahead will rest with the players.