Twice in three months, Francis has talked about changes to the tradition of celibate priests - although he has never been precise about how exactly this could be reformed.
Earlier this year, 26 women who said they were in love with priests living in Italy, wrote an open letter to the pope asking for a Vatican audience and speaking of their "suffering" because of the secret lives they have to lead.
Vatican expert Andrea Tornielli said at the time that Francis was particularly sensitive to the issue as, when he was the archbishop of Buenos Aires, he was close to an Argentine bishop who renounced the priesthood for love.
On a flight back from his recent trip to the Middle East, Francis pointed out that there were already married priests in the Ukrainian Greek Catholic and Coptic Catholic churches.
"The door is always open but we are not talking about it now as the order of the day," the Argentine pontiff said.
It is a priority, however, for the dozens of campaign groups that have sprung up - many formed by men who have been forced to leave the priesthood to get married.
The European Federation of Married Catholic Priests estimated more than 100,000 former Catholic priests have got married over the years - a figure which would make up around a quarter of the number of current priests.
The pope's comments over the weekend have had the effect of a new bombshell after La Repubblica daily in an interview quoted him as saying on priestly celibacy: "There are solutions and I will find them."
The comments were immediately denied by Vatican spokesman Federico Lombardi who said that the interviewer - the newspaper's 90-year-old founder, Eugenio Scalfari - had not written down the exact quotations.
"This is not at all an interview in the normal sense of the word," Lombardi said of the one-to-one conversation between Francis and Scalfari, even accusing the newspaper of manipulating "naive readers" with inaccuracies.
It was the second time that a papal interview with Scalfari has raised some hackles in the Vatican, leading to the question of whether the pope could be using these conservations as a way of bypassing traditional Vatican communications.
Father Papas Jani Pecoraro, an Italy-based married priest from the Greek Byzantine church, which is under Vatican authority, welcomed the pope's reported comments.
Speaking to La Repubblica, he said: "The issue could not only change the relationship between the Catholic Church and the lay world but also with other churches."
"We have to read the times and there is no doubt that today's society raises questions that a married priest is definitely better able to cope with," he said.
A Vatican expert, who spoke on condition of anonymity, said that as a whole Francis was seen as "an open pope".
"With his arrival, the progressives in the Church have regained hope," he said.
But a Vatican source said that merely pointing out that priestly celibacy is not a dogma was "no great discovery" and called for greater caution on over-interpreting papal comments.
The source said: "Some questions have been raised but this should not be seen as messages being passed on."
In the Repubblica interview, Francis pointed out that the ban on married priests was only instituted in the 10th century - nine centuries after the death of Jesus Christ.
"The pope is sensitive to the issue," said the Vatican expert, although many observers are puzzled as to what kinds of "solutions" the pope could have in mind and few are expecting major changes any time soon.