Pictured: Markle and Prince Harry attend a Wheelchair Tennis match during the Invictus Games 2017 at Nathan Philips Square on September 25, 2017 in Toronto.
Gambling company Ladbrokes closed betting that the couple would marry next year at odds of 4/6.
Understudy Megan, Nicky champion, who worked with her on this project, shared on Instagram a joint Markle picture and thanked her for her work.
A source told US Weekly: "Meghan has officially moved out of her Toronto apartment".
Talk of an engagement began to grow after Ms Markle, 36, announced she will no longer be appearing on the hit US TV legal drama Suits last week. However, there is no mention if the "Dater's Handbook" star attended Queen Elizabeth and Prince Philip's wedding anniversary on Monday.
Alex Apati of Ladbrokes said: "Punters are wondering who'll pop first - Harry with the question or Kate with the baby!" Movers were seen at her Toronto apartment, and now People is reporting that Markle is in the process of moving in with Prince Harry at Kensington Palace.
"As far as we're concerned, it's now a matter of when and not if Harry gets down on one knee this year".
It's been reported that broadcasters across the country are on standby for the announcement, which would likely follow the same format of the announcement of Prince William's engagement to Kate Middleton back in 2010.
The Duke and Duchess of Cambridge with Prince George and Princess Charlotte.
Prince Harry and Meghan Markle attend a Wheelchair Tennis match during the Invictus Games 2017
Meghan Markle is moving her dogs to London.
Markle first met Harry past year after being introduced by mutual friends.
She may even be planning to move into Harry's two-bedroom Nottingham Cottage.
Meghan Markle recently visited Rwanda as part of World Vision Canada.
It has been a year since Markle and Prince Harry first confirmed they are dating, but they have been rarely photographed together, save for some paparazzi photos.
Meghan Markle has reportedly wrapped up her time on "Suits" and felt nostalgic as she said goodbye to her cast and crew.
Markle was previously married to Trevor Engelson from 2011 - 2013.
Her arrival in the United Kingdom comes as speculation mounts over an imminent engagement between Meghan and Harry.