The region already represents 42 percent of the world's 1.2 billion-strong Catholic population, the largest single bloc in the Church.
"It would be good if there were candidates from Africa or South America at the next conclave," Swiss Cardinal Kurt Koch, head of the Vatican department for Christian unity said, referring to the closed-door election in the Vatican's Sistine Chapel.
The attraction of a non-European candidate would be in the change of style he could provide and the focus he could direct on issues closer to Catholics in developing countries.
While there are no official candidates, here are the "papabili" (potential popes) most frequently mentioned recently. The list is alphabetical, and could change before the conclave is held, most likely in March.
Joao Braz de Aviz, 65, Brazil: Supports the preference for the poor in Latin America's liberation theology, but not the excesses of its advocates.
Timothy Dolan, 62, United States: Named archbishop of New York in 2009. His humor and dynamism have impressed the Vatican. But cardinals are wary of a "superpower pope."
Marc Ouellet, 68, Canada: Effectively the Vatican's top staff director as head of the Congregation for Bishops. He once said becoming pope "would be a nightmare."
Gianfranco Ravasi, 70, Italy: Has been Vatican culture minister since 2007 and represents the church to the worlds of art, science, culture and even to atheists.
Leonardo Sandri, 69, Argentina: Born in Buenos Aires to Italian parents. He held the third-highest Vatican post as its chief of staff from 2000 to 2007.
Odilo Pedro Scherer, 63, Brazil: Latin America's strongest candidate. Archbishop of Sao Paulo, largest diocese in the largest Catholic country. Is conservative in his country but would rank as a moderate elsewhere.
Christoph Schoenborn, 67, Austria: A former student of Pope Benedict XVI. Ranked as papal material since editing the church catechism in the 1990s.
Angelo Scola, 71, Italy: Archbishop of Milan. Expert on bioethics. Also knows Islam as head of a foundation to promote Muslim-Christian understanding.