''My dad is on the Earth but I don't know where. He's still alive. If that sort of person dies, you could never make it a secret. The world changes if he dies," Omar told The Sun.
Omar, 29, who was once anointed by Osama as his successor to lead al-Qaeda, said he still loves his father.
"I still love him -- of course I do -- he's my father. That's a normal human situation. I miss him as a father but we are different. I want peace," he told the British newspaper.
Omar also spoke of his dream to date Hollywood star Drew Barrymore.
"My father said the only good thing to come out of America were weapons - like Stinger missiles. But I want to go to America and I would love to meet Drew Barrymore. I am single now and she is the most beautiful woman in Hollywood."
Omar also tried to clear the air about his split earlier this month from his British wife, Zaina -- a six-time married grandmother and 25 years his senior.
Zaina had allegedly said that Omar had begun to hear his father's voice in his head and was suffering from schizophrenia.
But, Omar said: "When people get angry and upset they say a lot of things they don't mean. I don't hear voices from my father in my head -- but I do dream about him a lot.
"The dream I have is that he is driving a truck and I stand in his way so he has to change direction. I hope to change his way for good, but it's only a dream.
"I admit I'm suffering from depression and taking anti-depressants because of the worry about my family, including two brothers being held in Iran for nine years.
"They are innocent. They are not terrorists but they are very down that they cannot leave Iran. I am very stressed and worried for them but I'm not schizophrenic."
The duo -- Omar and Zaina -- are now expecting a baby to be born from surrogate mother 24-year-old Louise Pollard. Omar wants to name the baby Osama, if he is a boy.
"If the baby is a boy I might call him Osama -- but I hope he will be peaceful in every respect. It's traditional to use the grandfather's name again.
"I prefer him to be in the Middle East with me. But wherever he is I will take care of him and take care of both his mothers - Louise as well as Zaina because she (Louise) is carrying my child. She is very pretty."
The junior Laden also spoke about his liking for Pop singer Madonna, Jim Carrey movies, American football, rock music and even Laurel And Hardy.
Omar was born to Osama's first wife, Najwa, in Saudi Arabia. The family moved to Sudan but his father was forced to flee as his terror group grew.
In May 1996, when Osama left for the Tora Bora mountains in Afghanistan, he chose Omar to accompany him and to set up terror training camps.
Omar said: "I was his chosen son. He's one of those people who has a magical effect for anyone who sits and listens. He changes minds. They said this also about Hitler. But I didn't follow my father."
Omar fled Afghanistan in April 2001 before the 9/11 terrorist attacks in the US that made his father the world's most wanted man.
