"It is coming already. I can see it. Look how many tragedies there are now with people killing each other all over the world for religious reasons," he said. "It won't happen in the near future, it won't happen while I am here, but it will happen again. I can actually see it in my vision."
Kleinman was 14 when he was taken to Auschwitz with his mother and seven brothers and sisters from a Romanian ghetto in May 1944. He never saw any of them again - or his father Martin, a rabbi, who they were told had been taken to work on the Russian front earlier that year, but in fact had also been taken to the death camp.
Kleinman, 84, was in Glasgow last week to speak to a group of 180 Scottish pupils about his experiences as part of the Holocaust Educational Trust programme. They heard his family were put into a freight wagon with more than 100 people and taken to Auschwitz.
"The children were screaming, it was so crowded. We didn't understand where we were going, but rumours started to circulate that we were going to Auschwitz," he said.
On arrival at Auschwitz, they were made to stand in a single line. A group of Polish Jews told Kleinman to pretend he was 17, saving him.
He said: "My mother and six of my brothers and sisters were sent to the left of the line. I was sent to the right. I had no idea where they had gone, but later other prisoners told me that they would have gone to be gassed and their bodies already cremated."
Kleinman, who lives in London, was showered and his prisoner number 8230 was tattooed on his arm. He was put to work on the camp's railroad tracks. What kept him going was the belief that his older sister, Gitta, may be alive, but he learned that she had died two days after liberation.
On April 23, 1945, Kleinman was liberated while on a death march to the concentration camp, Dachau. Despite his horrific experiences his message to pupils is one of compassion.
"For 60 years I never spoke about it. But I feel like it should never happen again and this is very important. It is not just Jewish people, it is other people who suffered as well. This is why I say to pupils that they should have compassion for each other and not hate each other," he said.
"The problem is that people forget the Holocaust. I do not hate the Germans and I do not hate anybody. We were not brought up that way.
"This is what I want to pass on because hate only causes hate. If I hate the Germans then what stops them from hating me back?"
Kleinman returned to Auschwitz as a free man on May 16, 2011, the anniversary of the day he arrived there as a prisoner 67 years earlier. There he lit nine candles and with a rabbi said Kaddish, the Jewish prayer of mourning, for the members of his family who died.