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He is also the father of Luis Roberto Alves, who would also go on to play for Club América and for the Mexican national football team because Luis Roberto was born in Mexico, during his father's playing days for América.
Vázquez received his first international call up for the Mexican national football team on January 23, 2014, under coach Miguel Herrera for a friendly match against South Korea held in the United States in preparation for the 2014 FIFA World Cup.