King also revealed the couple were still upset at the palace and claims no one from the royal family has reached out to Meghan, describing it as “frustrating”.
King said the royal family needs to “acknowledge there are issues” and said “right now, no one is”.
“Houston, we have a problem here. That’s really all they want. They want a conversation. They both want a conversation.”
“I’m not trying to break news, but I did actually call them to see how they were feeling, and it’s true, Harry has talked to his brother and he has talked to his father too,” King said.
“The word I was given was that those conversations were not productive. But they are glad that they have at least started a conversation.
“I think what is still upsetting to them is the palace keep saying they want to work it out privately, but yet, they believe these false stories are coming out that are very disparaging against Meghan, still.”
The insider details came as Harry’s grandfather, Prince Philip, emerged from a London hospital after a four-week stay and was reunited with the Queen at Windsor Castle.
William, just days ago at his first appearance since the interview, had said he had not spoken to Harry “but I will do” as he defended the royals and said: “We are very much not a racist family”.
King said the frustration from the couple came from the fact that the palace was saying one thing to the public but doing another in private.
“No one in the royal family has talked to Meghan yet, at this particular time,” she said.
“I think it’s frustrating for them to see that it’s a racial conversation about the Royal Family when all they wanted all along was for the royals to intervene and tell the press to stop with the unfair, inaccurate, false stories that definitely have a racial slant.”
King said it was “hard to move forward” for Harry and Meghan without a positive response from the family.
“Until you can acknowledge that, I think it’s going to be hard to move forward. But they both want to move forward with this and they both want healing in this family.
“At the end of the day, that is Harry’s family.”
The palace previously announced it would launch an investigation after The Times London reported that a former aide had made a bullying allegation against the Duchess of Sussex during her time as a working royal at Kensington Palace.
The investigation will now be led by an external law firm rather than the initial in-house inquiry the palace first announced.
On March 2, the outlet alleged that Meghan drove out two personal assistants and left staff feeling “humiliated”. Ms Markle’s team strongly refuted the allegations.
Then on March 3, Buckingham Palace said it was “clearly very concerned” about the allegations, and that the palace human resources team “will look into the circumstances outlined in the article” and would seek to speak to current and former staff.
King defended Meghan against the claims, saying “anyone who has worked with her will tell you exactly who she is”.
“You know, she’s really a very sweet, caring person. And as I say, Meghan has documents to back up everything that she said on Oprah’s interview. Everything.”
A statement from the Queen the day after the interview said she wanted the family to deal with the situation “privately”.
“The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan,” the statement read.
“The issues raised, particularly that of race, are concerning. While some recollections may vary, they are taken very seriously and will be addressed by the family privately.
“Harry, Meghan and Archie will always be much-loved family members.”
.@GayleKing checked in with Prince Harry & Meghan this weekend:
“Harry has talked to his brother and he has talked to his father, too. The word I was given was those conversations were not productive. But they are glad that they have at least started a conversation.” pic.twitter.com/fe0ATukkYw