According to the Daily Mail source, at least two permanent employees – a house manager and a cleaner – are being moved to other duties within the Queen’s household.
Other members of staff who are used on an ad hoc basis, such as chefs, maids and footmen, have been told their services are no longer required at the couple’s Windsor residence.
A source said: "The workers are already being offered other roles at Buckingham Palace.
"There is a skeleton staff there all the time, consisting of one cleaner and a house manager. Others work as and when needed.
"This has all come as a bit of shock. They took great pride in working for them and being at Frogmore."
While sources told the publication that no one is being made redundant because of the Duke and Duchess of Sussex's departure, there has been a knock-on effect on employees after their decision to relocate to North America for part of the year.
Harry and Meghan shocked the world on January 6 when they announced their decision to quit, and they left the royal family in a state of turmoil.
In a statement they said: "After many months of reflection and internal discussions, we have chosen to make a transition this year in starting to carve out a progressive new role within this institution."
They continued: "We intend to step back as 'senior' members of the Royal Family and work to become financially independent, while continuing to fully support Her Majesty The Queen. It is with your encouragement, particularly over the last few years, that we feel prepared to make this adjustment.
"We now plan to balance our time between the United Kingdom and North America, continuing to honour our duty to The Queen, the Commonwealth, and our patronages. This geographic balance will enable us to raise our son with an appreciation for the royal tradition into which he was born, while also providing our family with the space to focus on the next chapter, including the launch of our new charitable entity.
"We look forward to sharing the full details of this exciting next step in due course, as we continue to collaborate with Her Majesty The Queen, The Prince of Wales, The Duke of Cambridge and all relevant parties. Until then, please accept our deepest thanks for your continued support."
Queen Elizabeth was reportedly left "deeply upset" by the decision and began the task of fixing her family's future at a meeting at Sandringham on Monday, which involved Harry, Prince William and Prince Charles.
After the crisis talks, the Queen said she supported Prince Harry and Meghan's "desire to create a new life as a young family" in a statement.
“Today my family had very constructive discussions on the future of my grandson and his family,” the statement read.
“My family and I are entirely supportive of Harry and Meghan’s desire to create a new life as a young family.
“Although we would have preferred them to remain full-time working Members of the Royal Family, we respect and understand their wish to live a more independent life as a family while remaining a valued part of my family."