She is already a regular guest at his bachelor quarters and is on good terms with their neighbours, the Duke and Duchess of Cambridge.
She and Harry currently stay in Nottingham Cottage, a small two-bedroom house in the palace grounds.
The Suits star has met her prospective in-laws, the Prince of Wales and Duchess of Cornwall, and many believe they are "as good as engaged".
It is understood that Kensington Palace has been playing a key role in reducing the actress's publicity commitments to the TV legal drama Suits, an apparent clearing of the decks and part of what some are calling "Operation Princess".
The Mail on Sunday has learned that they have stalled an official announcement that Harry and Miss Markle would be making a public appearance together, fearing it would overshadow the 20th anniversary of Princess Diana's death.
Harry, along with his brother, has been a figurehead for a summer of national remembrance and celebration of his mother's legacy.
Meanwhile, Miss Markle's meeting with Charles and Camilla is felt to be particularly significant in her relationship with Harry.
"Harry's father is just keen for him to settle down and be happy," says a source. "Both Charles and Camilla are understood to have held back from expressing views, keen that Harry should have his own space to make his own decision."
One palace insider said: "Harry was nervous of introducing Meghan to them because he did not want people to jump to conclusions about someone he deeply cared for.
"He wanted to consider in his own time whether or not she might have a permanent place in his life."
Meghan is already friends with Harry's cousin Princess Eugenie and has forged warm relationships with those closest to him, such as his "second father" Mark Dyer, a former equerry to Prince Charles, who has mentored Harry since childhood.
That said, Royal protocol makes it unlikely that Meghan will meet the Queen until the official engagement announcement.
Meghan is thought by some senior courtiers to have already breached Royal etiquette with her recent Vanity Fair interview.
Her appearance on the magazine's cover to promote the 100th episode of Suits had been sanctioned by Prince Harry and Kensington Palace, but is said to have been greeted with surprise and dismay by Buckingham Palace.
There was also a photoshoot in which she was pictured in a black-and-white taffeta evening dress, an intriguing echo of a famous Snowdon portrait of Diana barefoot in an evening down.
Miss Markle told Vanity Fair: "We're a couple. We're in love. I'm sure there will be a time when we have to come forward and present ourselves and have stories to tell, but I hope what people will understand is that this is our time.
"This is for us. It's part of what makes it so special, that it's just ours. But we're happy. Personally, I love a great love story."
The comparatively intimate nature of the comments, combined with the fact the interview was to advertise a TV show, is thought to have caused concern to senior Royals.
But Miss Markle believed she had a professional responsibility to her television bosses and is set to give one further interview to a US publication.
After that, Buckingham Palace is likely to want to take a degree of control over the actress's public life, not least because of her background.
Meghan is three years older than Harry and a divorcee.
The fact that she is a divorcee also raises the spectre of Wallace Simpson, whose relationship with Edward VIII led him to abdicate, causing a constitutional crisis in 1936.
Prince Harry is fifth in line to the throne and will become sixth after the arrival of the Duke and Duchess's third child.
Marriage to Miss Markle would have no constitutional ramifications but the palace would wish to protect the public profile of a woman likely to become a full-time working Royal, and perhaps mother to a new generation of Royal children.
Miss Markle and the Prince met in June 2016 over drinks at Soho House, a London private members' club.
They managed to keep their romance secret for six months but have since been pictured going out privately in London, heading off on holiday, and attending a Caribbean wedding and a polo match together.
Born in Los Angeles, Meghan married film producer Trevor Engelson after seven years together, but the couple split two years later.
DIVORCED STAR WON'T MARRY AT ABBEY
As a divorcee (she split from her first husband in 2013), it is unlikely that Meghan would marry Harry in Westminster Abbey, which William and Kate used in 2011.
Nor are they likely to follow in the footsteps of the Prince and Princess of Wales, who married at St Paul's Cathedral in 1981.
Instead, they will probably consider St George's Chapel in the precincts of Windsor Castle, where the Earl and Countess of Wessex wed in 1999, and where the marriage of Prince Charles and the Duchess of Cornwall was blessed in 2005.
The couple might look north of the border to Canongate Kirk in Edinburgh, enabling them to host their reception at the Palace of Holyroodhouse like Princess Anne's daughter Zara did for her 2011 wedding to Mike Tindall.
Other possible venues include Crathie Kirk near Balmoral, venue for the 1992 second marriage of the Princess Royal to Vice Admiral Tim Laurence, or St Mary Magdalene in Sandringham, Norfolk.
