The Times newspaper has reported allegations that during her time as a working Royal, Ms Markle drove out two personal assistants and staff were "humiliated" on several occasions.
A complaint into this was made in October 2018 by Jason Knauf, then the Sussex’s communications secretary, the Times newspaper reported.
The paper claims that a number of sources told them that Ms Markle wanted to be a "victim" so her "unbearable experience" would convince Harry they had to leave the UK.
Her lawyers have denied this.
The monarchy's "men in grey suits" have been accused of being aware of the alleged actions of the duchess and of doing "absolutely nothing to protect people".
Buckingham Palace said in a statement: "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."
Addressing the bullying allegations, Ms Markle’s spokesman said the duchess is ‘saddened’ by the allegations.
The report comes just days before Meghan and Harry’s interview with Oprah Winfrey is due to be aired.