During his time with Callejas, he was called up by the Bolivia under-17s to play as their lone striker in the 2009 South American Under-17 Football Championship. He scored three goals in the tournament, including a double against Ecuador under-17s in the final group stage.
Later in 2009, as a 17-year-old, Álvarez was called up to the senior Bolivia side. He made his first senior international appearance as a substitute against Venezuela in a qualifying match for the 2010 FIFA World Cup on 6 June 2009. He gained a second cap the following year in a 5–0 friendly match defeat to Mexico in February 2010.
Álvarez comes from a large family, being the fifth of thirteen children. He harbours aspirations to play in Europe, declaring in a 2009 interview that he was delighted by reported interest in his signature from Lazio and that his ultimate ambition was to play for Manchester United.
