The princesses are also mentioned in emails, travelling with Ferguson, then known as Sarah, Duchess of York, to stay with Epstein shortly after his release from jail and asked to give his associates tours of the palace.
There is no suggestion of wrongdoing on their part, and they are said to have been left distraught by the allegations about their father.
Buckingham Palace declined to comment. Ascot did not respond to a request for comment.
A friend of the princesses suggested that it was too early for discussions about Ascot, and that no decisions had been made.
But all are understood to be mindful of their public appearances and how they will affect the public perception of the royal family.
The King has previously signalled his support for his nieces, and allowed them to walk with the royal family at Sandringham even after he stripped his brother Mountbatten-Windsor of his titles and honours.
They have previously attended garden parties at Buckingham Palace as well as Trooping the Colour, but are not expected to do so this year. They are not working members of the royal family.
One source said they were lying low and spending time with their own families while details of the Epstein scandal continue to unfold.
Mountbatten-Windsor is living at Wood Farm in Sandringham while he waits to learn whether Thames Valley Police will charge him with misconduct in public office.
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