It quoted Archbishop Stanislaw Dziwisz as relating how an American who was seriously ill received communion from the pope, and was cured.
The incident happened in 1998, but Dziwisz, who was John Paul II’s closest confidant for 40 years, spoke of the incident three years ago to reporters, who revealed it Sunday.
According to the report, Dziwisz told how an acquaintance had asked him if an American friend who was very ill with a brain tumor could meet the pope.
The acquaintance said the dying man had only three wishes: to see John Paul II, go on a pilgrimage to Jerusalem, and return to the United States to die.
"I remember him very well, his face showed he was ill," Dziwisz said. "I also remember that he had no hair, which was clearly due to the chemotherapy (treatment) he was having."
The pope, at the time at his Castelgandolfo retreat outside Rome, led a private mass at which the sick man received communion, the holiest part of the Roman Catholic ritual.
Later, Dziwisz’s acquaintance rang him to say that the man had been cured, "his tumor completely disappeared in just a few hours."
In his account of the incident, Dziwisz did not speak of a miracle but of a sign of "the supreme power of God" which surpassed human understanding.
La Stampa, however, pointed to the clamor at John Paul II’s funeral Friday for him to be made a saint, and said it could be interpreted as a miracle.
If he were to be canonised – he made more saints than all his predecessors combined – his case must pass three hurdles.
First is a ruling that he has led an exemplary life. Next is beatification following proof of a miracle as a result of his intercession.
The final stage, canonization, requires at least one more miracle.
Earlier this week, a Mexican teenager claimed the late pope had performed a "miracle" on him 15 years ago that cured his leukemia, while a nun in Colombia has said he cured her of an illness affecting her balance.
On Saturday, Vatican spokesman Joaquin Navarro-Valls pointed out in answer to a question on sainthood that it was up to the next pope to decide.
He said any such decision lay "in the sole competency" of the next pope.