A royal insider told the Evening Standard that, last Thursday, the pair arrived at the palace a little after 5 p.m.in a auto with blacked out windows and spent a little over an hour with Harry's gran.
According to reports, the actress is planning to give up her role as Rachel Zane in the courtroom drama, and told bosses the current season will be her last.
Meanwhile, Meghan, who has told studio bosses she wont be making another season of Suits, is preparing to spend more time in the United Kingdom, no doubt making plans for a rumored new apartment at Kensington Palace.
Prince Harry has taken Meghan Markle to meet the Queen, after she quit her job, prompting speculation they will announce their engagement.
Insiders say that Harry, 33, had spoken to his grandmother during the summer at Balmoral asking to introduce Meghan, who is three years his senior.
Last month, Harry and Meghan made their public debut as a couple at the Invictus Games in Toronto, where they held hands at a wheelchair tennis event.
In a recent interview with Vanity Fair, Markle confessed her love for Prince Harry, in her first comments about their relationship. She said that she and Harry were were "two people who are really happy and in love".
"We were very quietly dating for about six months before it became news, and I was working during that whole time, and the only thing that changed was people's perception". When they arrived, they were "whisked up to the Queen's private sitting room" for a one hour-long meeting. "I'm still the same person that I am, and I've never defined myself by my relationship".
"We're a couple", she explains.
We are sure Meghan absolutely nailed it though! It's part of what makes it so special, that it's just ours.