A complaint was made in October 2018 by Jason Knauf, then the Sussexes’ communications secretary, the Times newspaper reported.
The report comes just days before Meghan and Harry’s interview with Oprah Winfrey is due to be aired.
The complaint claimed Meghan had allegedly driven two personal assistants out of the household and was undermining the confidence of a third staff member, the newspaper said.
But her spokesman said: “The duchess is saddened by this latest attack on her character, particularly as someone who has been the target of bullying herself and is deeply committed to supporting those who have experienced pain and trauma.
“She is determined to continue her work building compassion around the world and will keep striving to set an example for doing what is right and doing what is good.”
Buckingham Palace did not comment and no-one from Kensington Palace was available for comment on Tuesday night.
The claims come as America is set to tune in to a new interview with the couple this weekend.
The CBS two-hour special will be screened on Sunday in the US and is expected to be shown in the UK on March 8.
ITV has won the bidding war to air the interview in the UK, with the network announcing on Good Morning Britain on Wednesday that it would be screening the programme next Monday. MailOnline has reported ITV’s deal to secure the rights is worth around £1 million.
The royal household will be braced for the show’s revelations as the couple discuss their life within the royal family and their exit from the working monarchy.
In dramatic promo clips, Winfrey asks Meghan if she was “silent or silenced”, with the duchess’s answer not revealed.
In response to a comment by the duchess, Winfrey asks: “Almost unsurvivable. Sounds like there was a breaking point?”
Harry is seen saying of his mother, Diana, Princess of Wales, while holding Meghan’s hand: “I’m just really relieved and happy to be sitting here, talking to you, with my wife by my side, because I can’t begin to imagine what it must have been like for her (Diana), going through this process by herself, all those years ago.”
At one point in the trailer, Winfrey tells viewers: “Just to make it clear to everybody, there is no subject that is off-limits,” as Meghan nods in agreement.
A PR expert has described the timing of the interview, with the Duke of Edinburgh currently unwell in hospital, as “horrendous”.
Public relations and crisis consultant Mark Borkowski warned that Harry and Meghan are at risk of a “real reputational mess” if they go ahead with the broadcast in the US on Sunday and said it should be postponed.
Harry’s grandfather Philip, 99, spent nearly two weeks in the private King Edward VII’s Hospital before being transferred to St Bartholomew’s Hospital on Monday for tests on a pre-existing heart condition.