The former talkshow host - who has interviewed stars such as Madonna, Victoria Beckham and Sir Paul McCartney in the past - told the Radio Times that the one person he would still like to chat with is Her Majesty.
"There's only one interview to be done and that's with the Queen," he explained. "What an interview that would be! Just imagine if it did [happen]! Where do you start? Where do you end? She's seen everybody. Nobody knows what she thinks.
"I'm not suggesting she should go on a talkshow," he continued, "but there should be some kind of record of her thoughts on everything she has been through and witnessed.
"She's an extraordinary woman - all the people she has met and the opinions she must have. She has seen most clearly of all what has happened to her country over the years."
Parkinson received an CBE in 2000 for his services to broadcasting and was later awarded an OBE in June 2008, describing it as a "very great honour".
He retired from television presenting in 2007 after 25 years fronting his own primetime show.