The couple, who have been married for over two years and are parents to 23-month-old son Flynn, apparently decided to "take a break", In Touch magazine claimed.
But a spokesman for the pair denied their romance was on the rocks, telling The Sun: "They're spending the holidays together."
British actor Orlando has been in South Africa shooting his new film Zulu, while his Australian model wife has been jetting around the world.
Miranda, who has modelled for Victoria's Secret, recently denied she was pregnant with her second child, writing on Twitter: "Someone hacked my account. It's ridiculous! I'm not pregnant!"