According to the publication, Meghan's alleged behaviour has also "driven a wedge" between Harry and his older brother Prince William.
The siblings have decided to split their joint royal household into separate entities.
"The Queen is fuming", the National Enquirer's palace insider adds.
The news also comes after Harry and his pregnant wife decided to move out of Kensington Palace.
The couple, who are expecting their first child together in 2019, are moving to Windsor Castle's Frogmore House.
In a statement released to PEOPLE, their office said, “The Duke and Duchess of Sussex will move to Frogmore Cottage on the Windsor Estate early next year as they prepare for the arrival of their first child. The couple have lived at Nottingham Cottage since their engagement last year.”
“Windsor is a very special place for Their Royal Highnesses and they are grateful that their official residence will be on the estate,” the statement continued. “The Duke and Duchess’s official office will continue to be based at Kensington Palace.”
The Royal Family is yet to respond to the National Enquirer.