The 36-year-old former American actress -- who'll turn 37 Saturday -- tied the knot with Britain’s Prince Harry, 33, in May.
Burrell, 60, previously served as a footman to Harry’s grandmother, Queen Elizabeth II, before he began working for Diana, the late Princess of Wales.
“It’s interesting that Meghan has just joined the biggest soap opera in the world and she has just landed the biggest role of her life as an actress,” Burrell told Yahoo News’ weekly six-part series, "The Royal Box," Friday. “I think, yes, she did want to be famous, she’s got everything that she wanted, but I [also] think ‘be careful what you wish for’ because sometimes it’s not all that it seems.”
“Diana found that out at an early age,” he added. “To be a royal princess sometimes, losing your anonymity, losing that freedom, that’s a big ask for any woman in today’s society.”
And while the couple recently tied the knot, Burrell insisted Markle will be expected to help expand the royal family.
“I predict that Meghan will very soon have a baby,” he said. “They will have a baby within the first year of their marriage. Well, she will be pregnant within the first year of their marriage. Time is marching on and Harry does want a family. I think there’s not much time left for Meghan. She’s got to get on with it. Two [children] will be enough for Harry.”
One of the main reasons Markle will struggle to find her place in the palace is because her family in America isn’t getting the support they need to cope with the constant media scrutiny.
Markle’s father, former Hollywood lighting director Thomas Markle, has particularly faced backlash by the public for repeatedly speaking out to the press about his famous daughter.
“There is no protocol for people like Thomas Markle, or in-laws, and people who marry into the royal family are lost at sea,” said Burrell. “They have embraced Meghan, they are keeping Meghan safe, but how about all the people in her world? I think they need to think about this, it’s a problem.
"Poor Thomas Markle doesn’t know how to behave. He is lost. I think the best thing he could do is stay quiet and try and reach out to his daughter. Somebody has to fix it. Before it gets more broken. Thankfully, Meghan’s mother has survived with dignity and style and that’s the way forward.”
This isn’t the first time Burrell has slammed the royal family for not protecting Thomas against the media.
Back in June, Burrell told ITV’s “Good Morning Britain” he wondered why the palace hasn’t been informed about Thomas speaking to the media for pay.
“The palace has the biggest PR machine in the world and they can’t protect those who are outside the gates,” he explained. “There’s no protocol in place, it’s never been done before. They don’t look after those coming into the family. The outsiders are the ones who are most vulnerable and that’s what I saw in the interview.
Still, Burrell believed Thomas has meant no harm in sharing his experience with the world.
“I like him,” he said. “I thought he was vulnerable. I felt sorry for him and I know what’s going to happen. The world press are on his doorstep and now they want more. What’s next? Is [Markle’s mother] Doria (Ragland) going to sit here talking about swapping knitting patterns with the queen?”
Back in May, Thomas, 74, debunked claims that he asked his daughter for money just weeks before the wedding.
Thomas told TMZ the rumor is “just plain bulls---.” Thomas alleged he has “a decent retirement fund” and doesn’t need his daughter’s help for money.
Thomas added that if he did ever need financial assistance, he is certain Markle would come to the rescue. Thomas also claimed money has never been a topic of discussion between the two and neither brings it up.