The King plans to make Princess Charlotte the Duchess of Edinburgh instead of giving the title to the Earl of Wessex, according to reports.
While it was anticipated Edward would inherit the dukedom after his father's death last year, the King has allegedly held back the title for his granddaughter.
Insiders claim that giving the senior royal role to Charlotte will be a tribute to his late mother, Queen Elizabeth II, who also had the title.
Sources told The Mail on Sunday: "Discussions are under way, but the favoured outcome for the King is that this title ought to go to Princess Charlotte.
'It would be a fitting way to remember the Queen - who, of course, had the title Duchess of Edinburgh - and a way for His Majesty to honour the line of succession."
Charlotte is third in line to the throne, after her father, the Prince of Wales; and elder brother Prince George.
The ancient rule of royal primogeniture, which gave men precedence over women in the line of succession, was scrapped under the Succession to the Crown Act in 2013.
It meant Charlotte's position was not impacted when her younger brother, Prince Louis, was born in 2018. By contrast, while Princess Anne, the Princess Royal, was the second child of Prince Philip and Queen Elizabeth II, her younger brothers, Princes Andrew and Edward, were above her in order of succession.
Charlotte's position will only change if Prince George has children.
If granted the title, Charlotte will be the fourth member of the Royal family to have been given the position since it was first created in 1726.
An insider said: "Charlotte's position is historically significant because she is the first female member of the Royal family whose place in the line of succession will not be surpassed by her younger brother.
"So it is constitutionally significant that Charlotte should be given such a corresponding title, because it is not beyond the realms of possibility that she will accede the throne if, for example, Prince George does not have children."
It was widely assumed Edward, the third son of the late Queen and Prince Philip, would become the Duke of Edinburgh.
He was made Earl of Wessex upon his marriage, while his brothers were given dukedoms.
In what was seen as a sign he was preparing for the rank, he took over as the chairman of the trustees of the Duke of Edinburgh Awards in 2015, the scheme founded by his father in 1956.
But Charles III has been planning a slimmed-down monarchy, which sources said is "about promoting those directly in line to the throne rather than those on the edges."
A source close to Edward said it "had not gone unnoticed" that he had not been granted the title.
A Buckingham Palace spokesman said no decision had been made.