Thomas Markle – who has not met the Prince – also claimed he himself was urged by the royal to “give Donald Trump a chance”
When asked about details of the Brexit conversation, he said: “It was just a loose conversation… I think he (the Duke of Sussex) was open to the experiment.”
A spokesperson for Kensington Palace had no comment on the claims.
Markle was unable to walk the Duchess of Sussex down the aisle after undergoing heart surgery just days before the wedding, but said he was “honoured” that Harry’s father, the Prince of Wales took on the job on his behalf.
“I can’t think of a better replacement,” he told the programme.
Markle’s operation came shortly after allegations surfaced that he had staged photographs with the paparazzi.
He said he had apologised to both Harry and Meghan for causing them embarrassment in the run up to the wedding.
“I realised it was a serious mistake. It’s hard to take it back,” he added.
Markle said that he opted to take part in the interview because he wanted people to know he is a “normal guy” and because he wants to have a good relationship with Meghan and Harry.
He said: “Over the last few weeks, everybody has had different opinions, some people said I was faking my heart attack, some people said I was skipping out, all kinds of stories were coming out about me, negative ones.
“But I just want people to know I’m a normal guy, I’m a retired man and I was living a quiet little life and this happened, and lots of things happened around it, and I’ve tried to survive through that, but more than anything I don’t want my daughter or new son-in-law to be hurt by any of this.
“I want to have a nice, normal relationship with my royal family as well now.”