Another insider reportedly told the US publication, 'All the signs have been there for months now.
'It's wonderful news to be sure - but it shouldn't come as a shock to anyone.'
The Enquirer's shocking report claims 36-year-old Meghan secretly visited fertility doctors before her May 19 wedding to Prince Harry, who is sixth in line to the British throne.
'Harry and Meghan want to get pregnant as quickly as possible after their wedding,' a friend tells.
'They both know that as Meghan gets older, it can get increasingly harder to conceive - and they are both keenly aware of her vulnerability to health complications and the chance of miscarriage the older she gets.'
Along with fertility check-ups, Meghan also visited London-based nutritionist Melanie Brown at Kensington Palace, insiders told the Enquirer.
Brown, a 'specialist in fertility, IVF, and pregnancy,' who works out of Duke Street, gave Meghan pointers on 'pre-conceptual and pregnancy nutrition, including weight loss and gain, and immune issues.'
Harry, 33, also reportedly 'stepped up', meeting with nutritionist Gabriela Peacock on how he can drop weight and boost fertility.
Meghan and Harry's exciting baby news will mark the first time the monarchy has welcomed twins in almost 600 years.
The Duke and Duchess of Sussex's twin joy may have been the help of his genetics.
Harry's uncle, his mother Princess Diana's brother, Charles Spencer, has identical twin daughters. The royal's great-grandfather, Edmund Maurice Burke Roche, the fourth Baron Fermoy, was also an identical twin.
One insider told the Enquirer, 'We all know where the genes for twins comes from - and it wasn't the House of Windsor on Harry's side!
'You might romantically say this is Diana's last gift to her youngest son.'
The royal family is yet to respond to the National Enquirer's report.