But media outlets have claimed that the Queen has put her foot down - saying she will not allow it.
"Meghan wants her baby to be raised a vegan," an unnamed 'palace insider' reportedly told Woman's Day.
But another source reportedly revealed to the publication: "It's created tense discussions between Meghan and Harry, who doesn't want to upset his grandmother.
"He's hoping Meghan will settle once the baby comes and he's putting this latest polarising idea down to heightened emotions while being pregnant."
Is Meghan vegan?
The Royal Family famously engages in multiple behaviors that cause animal suffering - including hunting and shooting. According to media reports, Prince Harry has ditched some hunts in a bid to appease Markle.
But there is no evidence to suggest that Markle is herself is actually vegan. Instead, it appears she is flexitarian - she revealed in a 2016 interview that she eats a 'part-time plant-based diet'. She said: "When I'm filming, I'm conscious of what I eat.
"I try to eat vegan during the week and then have a little bit more flexibility with what I dig into on the weekends. But at the same time, it’s all about balance."
She refuses to wear fur and often opts for vegan fashion choices - last year Markle spotted wearing a pair of animal-free Adidas Stan Smith trainers made by Stella McCartney.
Another fashion choice she opts for is vegan leather trousers. In an interview the former Suits actor did with Good Housekeeping magazine, the star spoke about her penchant for the fabric.
She said: "My wardrobe for my part in Suits isn't like Working Girl – dressing for work doesn't have to be so on-the-nose these days...personally, I love cropped pants in vegan leather, a great fitted blazer and a button-down [shirt]."
Kensington Palace has so far declined to comment.