Catholic nation Brazil is the epicentre of an outbreak of the mosquito-borne virus, which the World Health Organisation has called "an extraordinary event and public health threat".
Researchers have pointed to a suspected link between pregnant women's infection and a rare birth defect in babies.
It has led to calls for the Church's ban on contraception to be relaxed to prevent the spread of the virus or a baby being born deformed.
The Vatican has been asked for comment by several media organisations but has not replied.
It has meant individual Catholic leaders in the affected countries have made their own opinion clear.
"Nothing justifies an abortion," Revd Luciano Brito, a spokesman for the Archdiocese of Olinda and Recife in Brazil, told the New York Times.
He said that "just because a foetus has microcephaly won't make us favourable" to abortion.
The Catholic Church is against contraception because it believes it stops procreation.
The lack of official Church advice has led to the El Salvador government advising woman to abstain from sex until 2018 in a bid to prevent pregnancy.
Officials in Colombia and Ecuador have told woman to put off pregnancy until further notice.