Her interview with the couple will air in the U.S. on Sunday, and in the United Kingdom on ITV on Monday at 21:00 GMT.
Piers is responding to the alleged multiple complaints from members of her staff during Meghan's time as a working Royal.
When Prince Harry met Meghan in 2016, she was an actress in the successful United States drama Suits.
In the clip released on Wednesday night, Winfrey asks Meghan: "How do you feel about the palace hearing you speak your truth today?"
The allegations of bullying levelled at Meghan were published after the interview with Winfrey was recorded.
"The Firm" is a term which the Royal Family is said to use about themselves.
At the beginning of 2020, the couple announced that they meant to "step back" from these duties alongside their move to North America, with plans to review the arrangement after 12 months.
Meanwhile, The Times reported on Tuesday that Royal aides hit back at Meghan, alleging she faced a bullying complaint in October 2018 made by the couple's then communications chief, Jason Knauf. "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 palace said.
Reuters could not independently verify the report.
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He told reporters after having his bail extended Sunday that he was asked to report to the police again in early May. At the time of the Hong Kong vote, the United States Democratic primary, which Biden won, was still ongoing.
"We are clearly very concerned about allegations in The Times following claims made by former staff of The Duke and Duchess of Sussex", the palace said in a statement.
"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".
"Accordingly our HR team will look into the circumstances outlined in the article", the statement said.
Her spokesman said the duchess was "saddened" by the "latest attack on her character".
There's also concern regarding the interview because of what Prince Harry and Meghan Markle might say.
With explosive bullying accusations pinned against Prince Harry and Meghan Markle, it was expected that a formal investigation would be conducted however, the lack of response from the royal family indicates that the allegations were likely baseless, as per a report. Buckingham Palace confirmed last month that they had agreed with Queen Elizabeth II, Harry's grandmother, that they would not be returning as working royals.
However, at the same time "Meghan had to be told it was not the done thing when you are a member of the royal family".
In court documents submitted as part of her successful privacy action against the mass-circulation Mail on Sunday, her lawyers said she had felt "unprotected" while she was pregnant with their son Archie.
CBS has said Meghan will be interviewed about "stepping into life as a royal, marriage, motherhood" and "how she is handling life under intense public pressure".