It comes after the Sussexes, Prince Harry, 37, and Duchess Meghan, 41, stopped using their own HRH styles after they stepped down as senior working royals for a life in America.
Archie, 3, is technically history's first Prince of Sussex and 1-year-old Lili the first Princess of Sussex.
The claim about their HRH titles comes amid a major shuffle in the line of succession to the UK throne in light of Queen Elizabeth's death aged 96 at her home in Balmoral.
The Duke of Cambridge is expected to become the Prince of Wales after his father was named King Charles III, MailOnline also reports.
Prince William, 40, is now heir to the throne of the United Kingdom after Prince Charles' accession following the Queen's death.
The royal's wife the Duchess of Cambridge, 40, is also set to take on the new title of the Princess of Wales, according to MailOnline.
William is the oldest of the royals among the top eight in line, and is followed by his three children Prince George, 9, Princess Charlotte, 9, and Prince Louis, 4.
Following the Cambridges are the Duke of Sussex, as well as his children Archie and Lilibet, followed by Prince Andrew and his two daughters Princesses Beatrice and Eugenie of York.
The update is expected as the Prince of Wales title is not Charles' per se, but is conferred on the heir apparent, who then vacates the honour when he ascends to the throne.
