The former Vatican chief's letters to writer Anna-Teresa Tymieniecka, which feature in the documentary being shown by the BBC today, had been kept away from public view in the National Library of Poland for years.
The letters do not indicate that the Pope, who died in 2005 at the age of 84 , broke his vow of celibacy, but the tone of some of his letters to her points to intense feelings between them, the broadcaster said.
The then 50-year-old travelled from the US to Poland to discuss the work.
Shortly afterwards, the pair began to correspond. At first the cardinal's letters were formal, but as their friendship grew, they become more intimate.
The two spent camping and skiing holidays together and went on country walks.
"Here is one of the handful of transcendentally great figures in public life in the 20th Century, the head of the Catholic Church, in an intense relationship with an attractive woman," Eamon Duffy, Professor of the History of Christianity at Cambridge University, told the BBC.
She appeared to have revealed intense feelings for him because his letters immediately afterwards suggest a man struggling to make sense of their friendship in Christian terms.
In a letter dated September 1976, the pontiff writes: "My dear Teresa, I have received all three letters. You write about being torn apart, but I could find no answer to these words."
He goes on to describe her as a "gift from God".
The BBC has only seen John Paul II's letters, not Tymieniecka's side of the correspondence. She died in 2014.
But they were not with the Pope's letters when the BBC was shown them.
The National Library of Poland has not confirmed that they have Tymieniecka's letters.
The letters revealed that Cardinal Wojtyla gave Tymieniecka one of his most treasured possessions, an item known as a scapular - a small devotional necklace worn around the shoulders.
John Paul II was pope from 1978 to 2005 and was made a saint by the Catholic Church after his death.
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