The documentation about his life in Poland is completed and the documentation in Rome is almost finished, said the cardinal in an interview broadcast on Italian state radio on Sunday.
"I am happy because the cause (for beatification) is proceeding well," Cardinal said. "The Holy Father Benedict XVI is looking after it."
"I'm not in a hurry .... People are discovering, even those who before watched with curiosity ... the true face of John Paul II and his heritage," Dziwisz said.
Cardinal Dziwisz was named archbishop of Krakow after John Paul died in 2005.
Pope Benedict XVI waived the five-year waiting period after a person's death to begin a case for possible sainthood. Pope John Paul II lifted a similar waiver for Mother Teresa in 2003.
The Sunday Times of London reported that the three miracles required for sainthood have already been reported in the case of John Paul II.
The British newspaper reported that the cardinal overseeing the John Paul’s beatification process said he expected the local dioceses to have checked on the three miracles by April. A formal announcement is expected on April 2, the second anniversary of John Paul's death, he reportedly said.
"In Krakow, the procedures were wrapped up quickly because there were fewer witness, there are more in Rome (with) 27 years of papacy," the cardinal said. "But it seems that this questioning process is nearing completion also in Rome, and then after that it is in the hands of the Holy See."
Recalling John Paul's last days, as the pope drew near death in the Apostolic Palace on St. Peter's Square, the cardinal said that the pontiff could hear the prayers and songs of faithful gathered below outside the apartment studio window. "Up there, you heard everything, ... the words from the square."
Dziwisz said that during his papacy John Paul would go into the chapel near his bedroom to pray. "He always had this habit. Every night before going to bed, he went into the chapel, and after he would go to the window. Always, until the last day, he was trying to raise himself up in bed to see Rome, to bless it. Because it was his city."
One of the miracles John Paul is being credited with is curing a French nun of Parkinson's disease. The late pope also suffered from the disease. The nun was in the advanced stages of Parkinson's when members of her convent prayed to John Paul to ask God for her recovery in May 2005.
.- The cause for beatification for Pope John Paul II is advancing well, says the late pontiff’s personal secretary, Cardinal Stanislaw Dziwisz.