The Daily Mail quoted sources as saying Buckingham Palace has buried a report on claims from Meghan Markle's staff.
According to the publication, Queen Elizabeth paid for the investigation by a private firm.
It said the decision not to release the report was made to heal a rift within the royal family.
Senior royal biographer and commentator Angela Levin is not happy with the Palace's decision.
Levine, who is known to be a pro-monarchy royal expert, said: "By not publishing it we will all be guessing and waiting for someone to leak it sooner or later."
Meghan Markle recently met the Queen twice.
She met the monarch on her way to the Netherlands for the Invictus Games for the first time since leaving Britain.
She then traveled to the UK with her husband Prince Harry and two children to attend the Queen's Platinum Jubilee celebrations.