A man from Chile has spoken with a Spanish newspaper about a conversation he had with the Catholic leader three weeks ago.
Juan Carlos Cruz told El Pais: "He told me, 'Juan Carlos, that you are gay does not matter. God made you like that, and he loves you like that - and I do not care.'
"The pope loves you as you are. You have to be happy with who you are."
The Vatican has neither confirmed nor declined the alleged comments.
Pope Francis also offered Mr Cruz an apology for the sexual abuse he had suffered at the hands of Catholic priests, including the notorious paedophile Fr Fernando Karadima.
The Roman Catholic Church in Chile has been rocked by a sex abuse and cover-up scandal which last week saw all the country's 31 active bishops offer their resignation.
His latest comments may be interpreted as a fresh indication of the pontiff's commitment to seeing the Roman Catholic Church become more inclusive of people identifying as gay, lesbian or bisexual.
Speaking to reporters on a flight from Brazil in 2013, he affirmed the Church's stance that homosexual acts were sinful but homosexual orientation was not, adding that gay people should not be marginalised but rather integrated into society.
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