"There is no way of predicting that but I wouldn't be surprised," Quijano said in an interview Monday with PBS' "NewsHour."
The interviewer, Margaret Warner, asked if there was a new standard for bishops to meet in the way they handle clergy abuse cases.
"I think the standard is not new but it's being applied more rigorously than in the past," Levada said.
Levada, who once served as an archbishop in Oregon and California now holds the office previously held by the Pope. He called the crisis particularly grave.
"This is anything but being a good shepherd when you abuse children and you violate their innocence. This is a crisis, if you will, that I think caught most of us by surprise," Levada said. "One bishop told me 'This isn't the cruise I signed up for,' but that's in fact what has happened."
That surprise is likely to spark outrage among abuse victims who maintain their warnings to bishops went unheeded for years. Levada was asked how many times pedophile priests had been moved.
"Well the question about how many times priests were transferred is not something that we have here," Levada answered. "It may be included in the file or it may not."
But would the church ever publicize their names?
"The names are public," Levada said. "I mean they are public in the dioceses."
As for Pope Benedict, Levada noted his meetings with abuse victims should serve as an example for bishops. And is a public apology forthcoming?
"We'll have to wait and see, but I wouldn't be surprised," Levada said.