Did Padre Pio say that one day John Paul II would be Pope?

We had heard the same thing, but the answer to your question is No. Padre Pio never told John Paul II that he would be Pope. In an article in Inside the Vatican, John Paul II was asked about this and admitted that Padre Pio never told him this. But the myth was spread all around nevertheless. But Padre Pio did throw John Paul II out of the Confessional during his visit to San Giovanni Rotondo in 1947.

Antonio Pandiscia is the official biographer of Padre Pio and he was the only man allowed to interview him more than once. He said: “The current Pope [sic] went to San Giovanni Rotondo for the first time in 1947 shortly after his ordination. A witness, who has since passed away, told me that Padre Pio was brusque with the young Polish priest on that occasion. I think he could not accept the fact that the young Wojtyla (John Paul II) had worked in the theatre before becoming a priest.” (Inside the Vatican, August/September, 1996, p. 12.)