Francis said that, although giving priests in training the option to be celibate or not was "not the solution", he could turn to the so-called "veri probati" or "tested men" already involved in the church to bolster the number of priests.
"We need to consider if 'viri probati' could be a possibility", he said in an interview with German newspaper Die Zeit. "If so, we would need to determine what duties they could undertake, for example, in remote communities".
The Association of U.S. Catholic Priests welcomed the pope's comments.
The AP reported that Francis has maintained a friendship with the Argentine widow of a friend who left the priesthood to get married, and he spent a Friday mercy mission past year visiting men who had left the ministry to start families.
The Latin phrase viri probati is used to refer to married men of strong faith, who are often older with grown children.
"I mean, they've had to close handsome old parish churches because, not only do they have less priests, but I think they have less parishioners", churchgoer Anna Phelps said.
Some countries face a serious shortage of Catholic priests; and Pope Francis is trying to fix that. The resistance would be "not just grumbling" from people in the pews, he said.
"Whether married or unmarried, I feel that both sides of the fence can fulfill the obligation or becoming a priest of Jesus Chris", Monsignor Polando said. "Fears close doors, freedom opens them". However, the Pope confirmed on Friday to the Bishop of Cloyne, Dr William Crean, that he agreed with the earlier decision to reject Mr Duane's appeal against dismissal.
In the first major interview that Francis has given a German newspaper, the pope was asked whether he experienced moments in which he doubted the existence of God. After Pope Paul VI's visit in 1968 and Pope John Paul II's 1986 visit to 11 Colombian cities, Francis would become the third pontiff to visit.
But Francis has made a practice of polling ordinary Catholics, most significantly in the run-up to his 2014-2015 meetings on family issues.
In 2012, before he became pope, the then-Cardinal Jorge Bergoglio said that priestly celibacy is "a matter of discipline, not of faith".