In an interview with Newsweek magazine about his life and the future of the monarchy, he said: “We are not doing this for ourselves but for the greater good of the people.
“Is there any one of the Royal Family who wants to be king or queen? I don’t think so, but we will carry out our duties at the right time.”
Harry also spoke about walking behind his mother’s coffin as a 12-year-old and said no child “should be asked to do that under any circumstances”.
In 1997, the youngster joined his father, the Prince of Wales, his grandfather, the Duke of Edinburgh, 15-year-old brother, the Duke of Cambridge, and uncle, Earl Spencer, in a funeral procession through the streets of London for Diana, Princess of Wales.
He said: “My mother had just died, and I had to walk a long way behind her coffin, surrounded by thousands of people watching me while millions more did on television.
“I don’t think any child should be asked to do that, under any circumstances. I don’t think it would happen today.”
Harry praised Diana for playing a huge part in showing him an ordinary life.
He added that he did his own shopping, saying: “People would be amazed by the ordinary life William and I live.”
The prince, who is dating American actress Meghan Markle, said if he was lucky enough to have children he was determined they should have a relatively normal life, adding: “Even if I was king, I would do my own shopping.”
Asked whether he worried that an ordinary Royal Family would take away The Firm’s mystery, Harry replied: “It’s a tricky balancing act. We don’t want to dilute the magic ... The British public and the whole world need institutions like it.”
Newsweek reported that Harry said several times that he aches to be something other than Prince Harry and that he is in a rush to make something of his life and make a difference.
“I feel there is just a smallish window when people are interested in me before (William’s children Prince George and Princess Charlotte) take over, and I’ve got to make the most of it,” he said in the interview at Kensington Palace.
Harry has also appeared in a short broadcast by Forces TV in which he opened up about how his time in Afghanistan was the trigger for him to get help dealing with his mother’s death.
Harry, who served on two front line tours with the Army, was filmed in conversation with Paralympic medal winner and former Invictus Games captain Dave Henson.
He said Afghanistan was the moment he realised he had to deal with his problems and that the Invictus Games he set up for wounded service personnel had been ‘’a sort of cure’’.
Harry was recently praised by mental health charities for revealing he sought counselling as he confessed it was not until his late 20s that he processed his grief for Diana, who was killed in a car crash 20 years ago this year.