Sources claim Charles isn't so keen on letting it go to his brother Prince Edward, the Earl of Wessex, despite the fact he's waited 20 years to inherit his late father's title.
As it stands, the title of Duke of Edinburgh has been passed to Philip's oldest son Prince Charles following his death in keeping with royal tradition, however, the title has long been expected to then be passed to Edward.
In 1999, Buckingham Palace announced Edward would be given the title "in due course" with the blessing of both the Queen and Prince Philip. It is believed Philip and Charles agreed Edward would inherit the title following the passing of both Philip and the Queen.
"The Queen, the Duke of Edinburgh and the Prince of Wales have also agreed that Prince Edward should be given the Dukedom of Edinburgh in due course, when the present title held now by Prince Philip eventually reverts to the Crown," the statement read.
Following his marriage to Sophie Rhys-Jones that year, the Queen gave Edward the title of the earldom of Wessex, which he chose. Edward and Sophie are the only son and daughter-in-law of the Queen and Philip who are known as earl and countess rather than duke and duchess, though neither of Anne's husbands have had royal titles.
However, The Sunday Times reports Charles is considering breaking the pledge as he reassesses his own future.
"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," a source told the publication.
"Edinburgh won’t go to them [the Wessexes] as far as the prince is concerned," another said.
Following Philip's death, Charles, who is known as the Duke of Rothesay in Scotland, reportedly sought advice on whether or not he should start using the Edinburgh title. It is believed he was advised to continue using the Rothesay title as it is senior to the Edinburgh dukedom.
Edward is aware that he may or may not be given the dukedom. In an interview with the BBC last month to mark what would have been Philip's 100th birthday, he was asked, "You will be the next Duke of Edinburgh, when the Prince of Wales becomes king, that is quite something to take on?"
He responded, "It was fine in theory, ages ago when it was sort of a pipe dream of my father’s . . . and 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."
The Wessexes, who are believed to be very close with the Queen, recently spoke of Philip's request for Edward to take on the Edinburgh title after their engagement in 1999.
"We sat there slightly stunned," Sophie told The Daily Telegraph. "He literally came straight in and said, 'Right. I’d like it very much if you would consider that'."
In the same interview, Edward said "theoretically" the title should have gone to Prince Andrew, but the Queen had already conferred a dukedom on him. "It’s a very bittersweet role to take on because the only way the title can come to me is after both my parents have actually passed away," he said.
"My father was very keen that the title should continue, but he didn’t quite move quickly enough with Andrew, so it was us who he eventually had the conversation with. It was a lovely idea; a lovely thought."
Once Charles becomes king, the title will technically cease to exist and can then be recreated for someone else.
A Clarence House spokesman told The Sunday Times, "We do not comment on matters related to the accession. No final decisions have been made."
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