The Times newspaper says Meghan allegedly drove two personal assistants out of the household and undermined the confidence of a third member of staff.
Meghan's spokesman said it was the "latest attack on her character".
It comes before Meghan and Prince Harry's TV interview with Oprah Winfrey is due to be aired in the UK on Monday.
The duchess lived at Kensington Palace for nearly a year after her marriage to Prince Harry in May 2018.
According to the story in the Times, the complaint was made in October 2018.