The statement read: "We are clearly very concerned about allegations in the Times following claims made by former staff of the Duke and Duchess of Sussex.
"Accordingly our HR team will look into the circumstances outlined in the article. Members of staff involved at the time, including those who have left the Household, will be invited to participate to see if lessons can be learned.
"The Royal Household has had a Dignity at Work policy in place for a number of years and does not and will not tolerate bullying or harassment in the workplace."
However, lawyers working for Harry and Meghan said the claims are based on "misleading and harmful misinformation".
Meghan's 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."
The report comes just days before Meghan and Harry's two-hour interview with Oprah Winfrey is due to be aired.
In clips promoting the interview, Winfrey asks Meghan if she was "silent or silenced", with the duchess' 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, 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."
A PR expert has described the timing of the interview, with the Duke of Edinburgh currently unwell in hospital, as "horrendous".
