Here is an excerpt of an interview with Cardinal Arinze, during a group discussion of religious leaders from around the world, held at the Thanksgiving World Assembly in Dallas, Texas, March 1999. Cardinal Arinze addresses various questions; I have quoted the relevant portion below.
Arinze: "Nostra Aetate" (a document from the Second Vatican Council) says that God's grant of salvation includes not only Christians, but Jews, Muslims, Hindus and people of good will. That is, a person can be saved, can attain salvation, but on the condition that the person is open to God's action.
Robert Ashley, news director at a Dallas radio station: So was Jesus wrong when He said He was the way, the truth and the life?
Arinze: He was right. He IS the way, the truth and the life. If you believe that, you will become a Christian (audience laughter). Only God knows to what extent a person is sincere, what opportunities the person has, and how the person used those opportunities. Only God can assess all that, and He never appointed any of us part of that advisory council (more laughter).
If a person were to push what you said a little further and say, if you're not a Christian, you're not going to heaven, we'd regard that person as a fundamentalist … and theologically wrong. It is quite another matter to say that one religion is as good as another. That is, it doesn't matter to what religion you belong. Religion is not put together that way: You change the rules and change the goalposts if you can't score. No, no, no. (But we do) believe that every religion has elements that are true and noble and good. How will it work out? I can't tell you. But we know that Christ, who says, "I am the way, the truth and the light," died on the Cross for everyone.
I met in Pakistan a Muslim. People would go to him. He had a wonderful concept of the Koran. We were like two twins that had known one another from birth. And I was in admiration of this man's wisdom. I think that man will go to heaven. But I am not the one who opens the door (audience laughter).
Ashley: So you can still get to heaven without accepting Jesus?
Arinze: Expressly, yes. (He laughs with audience.)"
Cardinal Arinze recognizes that it is possible to find goodness in other religions, and that members of these religions can be saved even without expressly accepting Christ, even though he admits he does not know how this happens. This is consistent with Vatican II and Dominus Iesus, both of which said that non-christians could be saved, in a manner known only to God.
However, it is clear that Cardinal Arinze recognizes that the point of the documents was not to say "they can be saved, because in a manner known to God he will bring them to explicit faith in Christ," rather, in a manner known to God, even non-christians can be saved, without coming to explicit faith in Christ.