José María Muñagorri was born in Buenos Aires as the son of Basque parents, and at the age of three his family moved to Madrid for professional reasons, and he began to study and to practice football at the Nuestra Señora Colegio del Pilar, which once was one of the capital's football cradles, best known for being a breeding ground for players for Madrid FC in its first years of existence.

[2] Muñagorri played as a right winger and was often described as terrifying by his opponents and mathematical by his teammates, and as such, he played a fundamental role in helping Madrid reach the Copa del Rey final on two occasions (1924 and 1929), both ending in defeats, and he started on the former which they lost 0–1 to Real Unión, courtesy of a goal from José Echeveste.

[3] Muñagorri was a Real Madrid undisputed starter for nearly a decade, however, his career was heavily affected by serious injuries, which interrupted his formidable performances.

[4] On 17 May 1924, Muñagorri participated in another historic eleven of Real Madrid, the one that opened the Estadio Chamartín on the eve of the 1924 Summer Olympics, in a friendly against Newcastle, netting once in a 3–2 win.

Muñagorri immediately jumped into the water to help Peña and eventually the sailors hoisted them back up and everything was a scare.