Jewish organizations have criticized Pius, who is being considered for canonization, for failing to speak out against the persecution of Jews during World War II.
Abraham Skorka, a close friend of Francis, told the Sunday Times that the pope would fulfill his promise.
Pope Francis wrote about the issue in his book, "On Heaven and Earth."
"Opening the archives of the Shoah [Holocaust] seems reasonable," he wrote. "Let them be opened up and let everything be cleared up. Let it be seen if they could have done something [to help] and until what point they could have helped."
Jewish organizations and Holocaust survivors welcomed the news, the Jerusalem Post reported.
"This is something that we have been asking for and hoping for for decades," Menachem Rosensaft, the senior vice president of the American gathering of Jewish Holocaust survivors and their descendants, said. "It is yet another proof that pope Francis is an exceptional individual who repeatedly demonstrates great sensitivity and integrity."