In an interview with Germany's Die Zeit, Francis mulled the possibility of ordaining so-called Viri Probati, meaning religious married men of proven character.
"We have to give a thought to whether Viri Probati are a possibility. We then also need to determine which tasks they could take on, such as in isolated areas, for example," he said.
Calling priest shortages an "enormous problem," Francis said the question needed to be tackled "fearlessly."
In 2014, Erwin Kräutler, the bishop of Xingu in the Brazilian rainforest, said he had discussed the ordination of married men with Pope Francis. Bishop Kräutler complained that in his diocese, which counted 700,000 faithful, he had only 27 priests.
Latin America has the largest priest shortage, according to Paul Sullins, a sociology professor at the Catholic University of America.
Last year, there were more than 10,000 Catholics per priest in Brazil, which has the world's largest Catholic population, he said. Meanwhile in the United States, there were roughly 1,800 Catholics for every priest.
"We don't have a clergy shortage in global terms," Sullins said.
In his interview on Thursday, Francis made it clear he was not pushing to make celibacy optional for new priests.
"Voluntary celibacy is often discussed in this context, especially in places where there are shortages of clerics. But voluntary celibacy is not a solution," he said.
The pope has previously praised celibacy, stating: "For now, I am in favor of maintaining celibacy, with all the pros and cons that come with it, because in 10 centuries there have been more positive experiences than errors."
Francis has, however, said celibacy is more about church tradition than doctrine, recalling how it was an option until 1100.
In 2013, Archbishop Pietro Parolin, before he became Vatican secretary of state, said priestly celibacy was "not part of church dogma and the issue is open to discussion because it is an ecclesiastical tradition."
Eastern Catholic Churches allow the ordination of married men as priests, and in 2009, Pope
Pope John Paul II, responding to requests received from some priests and laity formerly or actually belonging to the Episcopal Church in the United States, had decided to make a special pastoral provision for their reception into full communion with the Catholic Church.
Pope Francis acknowledged the stress and loneliness of celibate life last year when he visited a group of former priests who left the church to get married and have children.
By pushing the church toward more open debate about married priests, Francis may anger Catholic conservatives who are already opposed to his move to offer communion to some divorcees who remarry in civil courts.
Since the church does not recognize civil divorce, it holds that anyone who remarries is living in sin.
"Even if it is restricted to areas like Amazonia, conservatives may see the ordaining of married men as the thin end of the wedge," said Marco Tosatti, a Vatican correspondent with Italy's La Stampa.
But Tostatti added that he was doubtful Francis would make changes.
"He says that we should reflect on the issue, but he has done nothing about it despite pressure from some within the church for three years, so I am not sure he will do anything now," he said.
Kington is a special correspondent.
2:15 p.m.: This article was updated with statistics on the number of priests serving in Brazil and the United States.