La Liga has asked permission from the Spanish Football Federation (RFEF) to move January’s fixture between Girona and La Liga champions Barcelona from Catalonia to Miami.
The RFEF, however, has said it cannot approve the move until it receives more information on the plans.
Real Madrid president Florentino Perez has come out against the idea, which has also met fierce opposition from the Spanish footballers' union (AFE).
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La Liga president Javier Tebas remains determined to make the game a reality, however, while stressing it is voluntary.
If Tebas's plans are finally approved, Eibar are ready to sign up for the next game in the United States, which would take place in the 2019/20 season.
"Of course we are in favour of it, we have sent an email to Javier Tebas telling him we want to play there," Rodriguez told reporters on Friday at the club’s Ipurua stadium.
“I think it’s a great opportunity for a club like Eibar, because you will have the attention of a place like the United States, which is hosting the World Cup (in 2026 alongside Mexico and Canada) and where the interest in football is increasing a lot.
"To go there and play a match against Barca and Real Madrid is a good opportunity for any club in La Liga."
Eibar are the smallest team in La Liga and are from a town of 27,000 inhabitants. Their stadium holds only 7,000 spectators and they were promoted to Spain’s top flight for the first time in 2014 and have remained there since.
Eibar have two supporters clubs in the U.S., in Indiana and Philadelphia, and travelled to the States in 2016 for friendly games against the Philadelphia Fury and New York Cosmos.
La Liga chief Tebas told Reuters this week that small clubs like Eibar are central to the plans to play outside of Spain, due to the logistical problems of compensating fans deprived of a home game.
"To have a game in the States you need the big clubs but you also need small clubs because otherwise it’s difficult to resolve the problem of the fans (who can’t go to the game)," Tebas said.
"It also helps the smaller clubs to position themselves in the United States and internationally, because playing a game outside your territory would have an impact around the world and help them to promote their brand."
(Reporting by Richard Martin; Editing by Toby Davis)
