Following his marriage to Sophie Rhys-Jones that year, Queen Elizabeth granted him the title of Earl of Wessex, which he chose himself.
But now Charles is reportedly considering whether to break that promise as he rethinks his own future, reports the Sunday Times.
A source close to Prince Charles told the outlet, "The prince is the Duke of Edinburgh as it stands, and it is up to him what happens to the title. It will not go to Edward."
Another claimed the title wouldn't go to the Wessexes as far as Charles was concerned.
The title of Duke of Edinburgh would merge with the crown when Charles gains the throne, meaning the new monarch will be able to give Edward the title.
It means Charles is left with the decision of whether to give the title to Edward, to another family member, or to leave it in abeyance.
Heraldry adviser to the royal family David White told the Sunday Times there was no urgent need for Charles to give Edward the title on his accession to the throne.
"George VI was the Duke of York and when he became king, the dukedom merged with the Crown. It wasn't granted again until Prince Andrew became Duke of York," he pointed out.
The Queen granted Prince Andrew the dukedom after his marriage to Sarah Ferguson in 1986.
Edward is reportedly aware of the uncertainty surrounding the title. He was asked in an interview with the BBC last month, "You will be the next Duke of Edinburgh, when the Prince of Wales becomes king, that is quite something to take on?"
He replied that it was "fine in theory".
"Of course it will depend on whether or not the Prince of Wales, when he becomes king, whether he'll do that, so we'll wait and see. So yes, it will be quite a challenge taking that on."
He noted that the granting of the title was "bittersweet" as it could only come to him after both his parents had passed away. He's already taken up a few of his father's patronages.
He's a trustee of the Duke of Edinburgh's Award scheme as well as a patron of the Edinburgh International Festival.
Prince Philip was granted the title of Duke of Edinburgh on the day of his marriage to Queen Elizabeth, November 20, 1947.
He was president, patron or member of more than 780 organisations.
When contacted by the Sunday Times, Clarence House spokesperson would not comment on matters related to the accession.
Buckingham Palace also declined to comment to the newspaper.