He said of himself and brother Prince William: "We want to make sure that there's something that she's remembered by and there's certainly not enough on the right scale in London or anywhere in the UK, that she's remembered for."
Prince Harry with HELLO!'s royal correspondent Emily Nash Photo: Twitter/@emynash
He added: "Something needs to be put in stone or in place as a memory. Every single day we still think about her, so it would be very fitting on the 20th anniversary to have something that is going to last forever and is a proper recognition of what she did when she was alive."
Harry also revealed how he persuaded hilarious video message with him to promote Invictus – his tournament for wounded and injured veterans – in which she dismisses a mock threat from President Obama and wife Michelle with a wry, "Oh, really? Please."
Harry said his grandmother the Queen had "great fun" filming the Invictus Games video Photo: Instagram
Harry told HELLO!: "She had great fun. And I think it was almost as though you could see that look in her face, at the age of 90, thinking, 'Why the hell does nobody ask me to do these things more often?’"
He added: "We did one take from two angles. She's the Queen, she's busy! You don't have more than 90 seconds to get that right. Also, she's so incredibly skilled, she only needs one take.
Harry said he was a "gibbering wreck" filming the video Photo: Emily Nash
"Meanwhile, I was like a gibbering wreck. I was more nervous than anyone else. I was like, 'We've got to get this right.' And she just dropped the mic! It was great fun and I hope everyone enjoyed it."