The actress's beloved dogs meanwhile are expected to follow her across the Atlantic at a later point.
The reports come after Meghan was photographed shopping in London on Tuesday as she prepares to spend Christmas with Harry, 33.
Wearing shades, she looked chic in tight black jeans, a grey jacket and matching wrap-around scarf.
The actress was seen leaving a Heidi Klein designer beachwear store, possibly hinting at a winter holiday in the sun.
Meghan was clutching a £2,000 ($3,900) Prada handbag and a shopping bag from Sarah Chapman, which specialises in skin care.
Her arrival in the UK comes as speculation mounts over an imminent engagement between Meghan and Harry.
In fact, some royal watchers believe Meghan and Harry, who confirmed their long-distance relationship a year ago, are already secretly engaged - and that wedding bells are just around the corner.
The American actress has just finished filming her seventh and final season of the US legal drama Suits, in which she stars as lawyer Rachel Zane, in Toronto.
In fact, Meghan's body double sparked mass excitement after posting a cryptic Instagram post just a few days ago.
Nicky Bursic - who has been Meghan's stand-in on Suits for two years - posted a goodbye and congratulations message to the star on the social network that fans have taken of proof that both Meghan has quit Suits and that she is preparing for a long-term future with the royal.
"It's been an absolute pleasure and honour being your 'STAND-IN' for the last 2 seasons," Nicky wrote. "Though I've been on @suits_usa for 6 years, the latter 2 has been my most memorable. Wishing you all the happiness in the world Bella."
She added a love heart emoji and one of a champagne glass toast alongside some highly revealing hashtags, #youdeserveitall #loveher.
The couple gave the biggest hint yet that an engagement announcement is imminent when they made their first official public appearance together at the Invictus Games in Toronto at the end of September.
The pair put on a loved-up display, flirting and holding hands as they watched wheelchair tennis.
Within hours of the couple stepping out together bookies Ladbrokes suspended betting on an imminent announcement of an engagement.
MailOnline has contacted Kensington Palace for comment.