The revelation came in a dozen conversations Francis had with French sociologist Dominique Wolton, who is writing a soon-to-be-published book.
It was not specified what the future pontiff wanted to explore in the sessions, which took place when he was 42.
La Stampa, an Italian daily, quoting some of the conversations, said Francis went to the analyst's home.
Francis was quoted as saying: "One day, when she was about to die, she called me. Not to receive the sacraments, since she was Jewish, but for a spiritual dialogue."
He added: "She was a good person. For six months she helped me a lot."
At the time, Francis was a Jesuit official in his native Argentina, which was ruled by a military dictatorship.
In the conversations with the author, Francis speaks highly of the positive influence women have had on his life.
"Those whom I have known helped me a lot when I needed to consult with them," Francis is quoted as saying.
The 81-year-old pope also speaks of his state of mind now.
"I feel free. Sure, I'm in a cage here at the Vatican, but not spiritually. Nothing makes me afraid."
What bothers him, he said, are people with straitjacket points of view.
He singled out "rigid priests who are afraid to communicate. It's a form of fundamentalism. Whenever I run into a rigid person, especially if young, I tell myself that he's sick".
But Francis concludes that "in reality, they are persons looking for security".
In past remarks, the pope has indicated he struggled with how to use authority in his first roles of leadership as a Jesuit.
The Catholic Church used to project a sense of mistrust regarding psychoanalysis but updated Vatican guidelines for use in training future priests describe psychologists as valuable in assessing the psychological health of candidates.
