The pope's purported remarks came during a meeting with top officials of the Latin American Conference of Religious (CLAR) on June 6.
During the meeting, Francis seemed to refer to the Vatican investigation of an American nuns' group, the Leadership Conference of Women Religious, while telling the Latin American delegates not to worry should they find themselves the target of a similar investigation.
"They will make mistakes, they will make a blunder, this will pass! Perhaps even a letter of the Congregation for the Doctrine [of the Faith] will arrive for you, telling you that you said such or such thing. ... But do not worry. Explain whatever you have to explain, but move forward."
In what was seen as one of the defining acts of Pope Benedict XVI's papacy, the Vatican's doctrinal office issued a "doctrinal assessment" that criticized the LCWR for not speaking out strongly enough against gay marriage, abortion and women's ordination.
A partial account of the meeting was published Sunday by the Chilean magazine Reflexion y Liberacion, and later translated into English by the Rorate Coeli website.
Francis also reportedly admitted the existence of a "gay lobby" within the Vatican, and confessed that he is "disorganized" when it comes to administrative matters such as reforming the Vatican Curia.
The Vatican's chief spokesman, Jesuit Fr. Federico Lombardi, said Tuesday that the meeting was "of a private nature" and "therefore, I have no statement to make on the content of the conversation."
According to the Reflexion y Liberacion account, which seems to consist of notes from the meeting rather than an actual word-for-word transcript, Francis admitted that his task as head of the church's central administration, the Roman Curia, is "difficult."
In the Curia there are "holy people," he said, but "there also is a stream of corruption." "The 'gay lobby' is mentioned, and it is true, it is there. ... We need to see what we can do."
Reports of a "gay lobby" appeared in the Italian press last year in the context of the so-called Vatileaks affair that led to the arrest of Pope Benedict XVI's personal butler for leaking confidential documents to the press.
Benedict tasked three retired cardinals to investigate the allegations of infighting and personal rivalries in the Curia revealed in the documents. Their report was passed on to Francis after his election in March.
According to the Rorate Coeli report, Francis also said "almost all Cardinals" asked for a reform of the Curia during the cardinals' closed-door meetings that preceded the conclave.