The Vatican declined to comment on the report but, if confirmed, it would be a striking statement of tolerance towards homosexuality, which the Church has condemned as an immoral disorder if it is actively practised.
In an interview published on Sunday, abuse victim Juan Carlos Cruz told El Pais that Pope Francis had told him during a meeting this month: "The fact that you are gay does not matter."
Cruz said Francis had also told him: "God made you this way and loves you this way, and it doesn't matter to me. The pope loves you this way, you must be happy the way you are."
After attending a crisis meeting with Francis about the cover-up last week, all of Chile's bishops offered to resign.
Since his election in 2013, the pope has dramatically shifted the language the Church has used about homosexuality, which was once seen as a taboo subject.
"When a person arrives before Jesus, Jesus certainly will not say: 'Go away because you are homosexual'," he said.
Francis's predecessor, Pope Benedict, wrote in 2005 that homosexuality was "a strong tendency ordered toward an intrinsic moral evil".
(Reporting by Julien Toyer; Editing by Kevin Liffey)
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