The Duchess of Sussex was reportedly sent the Chopard earrings by Mohammad bin Salman when she married Prince Harry.
She is said to have surprised staff by wearing them to a state dinner in Fiji in 2018, despite reports implicating the Saudi royal in the Khashoggi murder.
The Washington Post columnist was killed and dismembered inside the Saudi embassy in Istanbul, Turkey, on October 2 that year, as he was picking up documents allowing him to marry his fiancee.
A book written by The Times' royal correspondent Valentine Low claims that Kensington Palace was alerted about the earrings.
In an extract of 'Courtiers: The Hidden Power Behind the Crown', Mr Low writes: "When they had first appeared in the media after the Fiji dinner, staff in London responsible for registering details of all royal gifts had recognised them and alerted Kensington Palace."
He then quotes a source saying: "We made a decision not to confront Meghan and Harry on it, out of fear for what their reaction would be."
Lawyers previously said that Meghan was unaware of the rumours at the time.
The Duchess wore the earrings again at Prince Charles' 70th birthday party at Buckingham Palace on November 14, 2018.
At the time of the Fiji tour, reporters were told the earrings were "borrowed".
There is no suggestion that the Crown Prince gave the earrings to the Duchess personally, and she is not known to have ever met him.
Lawyers had said that Meghan was unaware of the rumours of the Crown Prince's involvement in the Khashoggi murder, and said all staff knew where the earrings were from.
Meghan has previously shown her support for woman's rights in Saudi Arabia, appearing alongside activist Loujain al-Hathloul in 2016.
The campaigner, who lobbied for women to be allowed to drive, was arrested in May 2018 - shortly before Meghan and Harry's wedding - and her family claim she was tortured.