The 49-year-old singer was the result of the late Beatles legend's first marriage to Cynthia Powell, and he admits he always delayed having children because he did not want to do the same things his parents did when they were young.
He said: ''I didn't want to follow certain things dad had done because dad's mother died when he was 17 and so on. So I didn't want to have children so early in life and I wanted to learn about life a little more ... I didn't want to make the same mistakes, basically.
''One can only hope I've learnt a little more and am a little wiser on that front. It was a different time for everybody.''
Julian - who was abandoned by his dad at the age of five after his parents divorced - has in recent years been collecting memorabilia related to his father and he is doing so in the hope he can one day show the items to his children, if he has them.
During an appearance on 'This Morning', he said: ''If I'm going to have a family I want to have things that belong to my family, that were part of history. Initially, I started collecting the more personal things that were related to me - postcards sent to me. At the time you don't think things sent to you are going to be 'memorabilia' in later life.''