Speaking to new! magazine about Harry and Meghan's approach towards Thomas Markle, the former butler said: "I've been in similar situations where people said things about Princess Diana, and the way she dealt with it was by freezing them out.
"It looks as if Harry has taken a leaf out of his mother's book. Diana said, 'Once someone burns the bridge of trust towards you it's very hard to repair it.'"
He added: "Harry is his mother's son and the apple doesn't fall far from the tree...
"She would be furious if someone betrayed her and the only way she could deal with it is to cut them off completely".
It comes after he previously commented on how Meghan might have longed for the fame that her new role has brought her, but that she should "be careful what she wishes for" as "sometimes it is not all that it seems".
In the interview for Yahoo News weekly six-part series, he also weighed in on the Royal Family's treatment of Thomas Markle, saying there is "no protocol" for dealing with in-laws.
Burrell said: "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."
The former butler also urged Meghan to "get on with" having a baby, describing how "time is marching on", and predicted that the duchess would fall pregnant in her first year of marriage.
Thomas Markle's media storm: How it unfolded
• November 27 2017: Kensington Palace announces the engagement of Prince Harry and Meghan Markle
• December 2017: Meghan's father Thomas Markle is pictured near his home in Rosarito, Mexico, going to Walmart and buying beers
• April 2018: In the run-up to the royal wedding, Thomas is pictured reading a book about landmarks of Britain, looking at pictures of the couple online, and being fitted for a suit
• May 2018: Mail on Sunday reveals Thomas Markle staged the paparazzi photos in a bid to improve his public image and may have made up to £100,000 from them. It was later revealed to be Samantha Markle's idea
• 17 May 2018: Bride-to-be Meghan reveals her father will not be flying to London for the wedding, after reports he suffered a heart attack
• 19 May 2018: Thomas Markle watches the wedding on TV from Mexico as the Prince of Wales steps in at the last minute to walk Meghan up the aisle
• 18 June 2018: Meghan's father gives his first TV interview with Good Morning Britain and leaks details of his private conversations with Harry and Meghan - including their desire to have children and Harry's views on President Trump
• 26 June 2018: Thomas Markle tells TMZ he feels he is being frozen out by the Palace and is insulted that he has not been invited to meet the Queen
• 5 July 2018: The Duchess of Sussex's father tells friends he fears their relationship is 'lost' forever and he may never see his daughter again
• 28 July 2018: Speaking to the Mail on Sunday, Thomas Markle says his daughter is ignoring him and has changed all her numbers since marrying Harry. He ominously warns he 'won't be silenced'
• 14 August 2018: In another interview with the Mail On Sunday, Thomas Markle claims he hung up on Prince Harry in a heated phone exchange
