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The couple, who have been dating for about a year, are being tipped as the next ones to walk down the aisle.
“Harry was being the perfect gentleman with Meghan,” an insider tells PEOPLE of the royal’s chivalrous behavior at Middleton’s lavish reception.
According to Majesty’s Ingrid Seward, the prince doesn’t want to “hurry things” before getting down on one knee.
“He wants her to acclimatize to it all,” Seward tells PEOPLE. “It’s such a whole different world to move into — there’s so much to get used to.”
She adds, “He’s really in love with her, but wants to give it his best crack.”
British bookmakers agree that a proposal is in the cards. Prince Harry is the frontrunner to be the next royal to wed, according to Ladbrokes.
As Markle made her appearance at Middleton’s high society wedding on Saturday, the bookies are now taking wagers on which member of the royal family will be getting married next, and all eyes are on Prince Harry as the favorite.
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Rival bookmakers William Hill believes that the coast is clear for Harry to propose to his girlfriend. As a result, the bookies have trimmed the price of a 2017 engagement from 3/1 to 2/1.
This year’s Invictus Games will take place in September in Toronto, where Markle lives while she’s filming her USA legal drama, Suits.
Markle is also getting back to business. She’s scheduled to attend a Suits panel at the ATX Television Festival in Austin, which will take place June 8-11.
The couple, who travel back and forth between Toronto and Buckingham Palace, are good about finding time to spend with each other in between their busy schedules.
And in April, Harry flew out to Toronto (where Markle films Suits) to spend Easter weekend with his girlfriend — skipping the usual royal Easter tradition of attending services at St. George’s chapel at Windsor castle with Queen Elizabeth II.
“Despite the distance, the media attention and everything else, there’s a real ease to their relationship,” a source recently told PEOPLE. “It just works. They are deeply happy.”
- With reporting by Simon Perry