The call for study on the proposal was contained in the working document, released on Monday, for an October meeting of South American bishops on the Amazon.
The document, prepared by the Vatican based on input from the region, affirmed that celibacy is a gift for the Catholic Church.
But it suggested officials study "the possibility of priestly ordination for older men, preferably indigenous and respected and accepted by their communities, even if they have stable families, for the region's most remote areas".
The idea of ordaining so-called "viri probati" - married men of proven virtue - has been around for decades to cope with a priest shortage and decline in vocations overall.
But it has drawn fresh attention under Pope Francis, history's first Latin American pope, thanks to his familiarity with the challenges facing the Amazon church.
The October 6-27 meeting on the sacramental and environmental needs of the Amazon will draw bishops from Bolivia, Brazil, Colombia, Ecuador, French Guiana, Guyana, Peru, Suriname and Venezuela.
Brazil's bishops have long pushed for the Church to consider ordaining viri probati to minister in remote parts of the Amazon where by some estimates there is one priest for every 10,000 Catholics.
The celibacy question has been a mainstay in Catholic debate given it is a discipline, not a doctrine, and therefore can change.
The Church has had the tradition since the 11th century, imposed in part to spare the Church the financial burdens of providing for large families and to ensure that any assets of the priest would pass to the Church, not his heirs.
Proponents of a relaxation of the rule say more men would consider a vocation to the priesthood if they could marry, a surefire fix to the decline in priests globally.
Opponents say relaxing the rule for the Amazon will certainly fuel calls for it to be relaxed elsewhere.
Already, married men can be ordained in the Eastern rite Catholic Church and married men who convert from Protestant churches can be Catholic priests.
In addition to ordaining married men, the document called for the synod to identify "the type of official ministry that can be conferred on women".
It said women, who already play important roles in indigenous communities, must be guaranteed leadership roles.
But it stopped short of recommending debate on whether women could be ordained as deacons.
One of the organisers, Monsignor Fabio Fabene, said the female diaconate was essentially off the table since Francis has recently determined that the issue needs further discussion.
Overall, the synod bishops are expected to debate a host of measures to better minister to indigenous and migrant communities in the Amazon amid deforestation and exploitative industries and competition for souls from Pentecostal churches, which are more present in the region with indigenous, local leaders.
The Vatican's working document acknowledged this competition, saying the Catholic Church must transition from being a church that merely visits vast regions to one that has a full-time presence with ministries, liturgies, sacraments and social services.
It called for a Church that has a more indigenous face, with local songs, dance, costumes and the Bible translated into various languages.
What is needed, it said, is to essentially recover aspects of the primitive Christian Church.
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