Former and current royal aides who were unable to give evidence at a recent privacy court case regarding the duchess are expected to speak to investigators.
The Sussexes are not expected to be invited to take part in the inquiry, despite having written to the Palace about it, the paper reports.
Last month, two senior members of staff alleged that they were bullied by Meghan while another member of staff said they had been “humiliated” by the duchess.
Meghan has denied these allegations.
In 2018 Jason Knauf – the Sussexes’ then communications secretary who now heads the Duke and Duchess of Cambridge’s charitable foundation – made a bullying complaint in an apparent attempt to force Buckingham Palace to protect staff.
In an email to a senior courtier he said: “I am very concerned that the duchess was able to bully two PAs out of the household in the past year.”
He described her behaviour as “totally unacceptable” and claimed she “seems intent on always having someone in her sights.”
The email was forwarded to the HR department but the complaint did not progress until this year.
The upcoming inquiry reportedly aims to “learn lessons” by taking evidence from members of staff past and present.
It is understood that the palace does not want it to “be played out in public” in order to ensure all those taking part “feel comfortable”.
It is thought the inquiry will begin soon, with no set time frame.
A royal source told the Times: “It will take as long as it will takes.”
A palace spokesman told the paper they are “committed” to looking into the circumstances around the allegations from former staff of the Duke and Duchess of Sussex and will not be providing a “public commentary on it”.
Meghan said she became suicidal during her time as a senior royal and said a family member had expressed concerns about her unborn son’s skin tone.
Buckingham Palace released a statement following the allegations and said while “some recollections may vary” they are taken “very seriously”, but would be addressed by the family privately.
On Saturday night, it emerged that William and Harry had “been in contact” for the first time since last Sunday’s televised interview, with sources claiming the brothers have since exchanged texts.