He told the show’s host Pandora Forsyth: “I’m sure the king would welcome them back. He’s quite keen to heal that family rift but it’s obviously very raw and very noticeable.
“While he’s keen to heal that rift he hasn’t met his son the last two times he’s been over to the UK.”
Mr Palmer added that an interesting question would be whether Harry and Meghan would be seen at Royal Ascot.
He added: “An interesting what-if question, ‘If he and Meghan were around would they be invited to Royal Ascot?’”
Mr Palmer’s comments come as Meghan’s popularity plummets to an all-time low according to a new poll.
Those who had a negative opinion of Meghan made up 68 percent of respondents while 21 percent had a positive opinion of the duchess according to the YouGov poll of 2,014 people.
The new data suggests that Meghan’s popularity has fallen by three points since April and added to the “total negative view”.
Prince Harry is also not in favour with the British public with 63 percent having a “total negative” view of the prince and just 28 percent having a positive view of him.
In contrast, King Charles is more popular than his youngest son. The data from the poll suggest around six in 10 have a positive view of the King.
His net favourability currently stands at 32 which is an improvement on April when it was just 26.
The results come just days after Harry and Meghan were dropped by Spotify which announced it would not be renewing its three-year deal with their production company, Archewell Audio.
The two businesses announced they had “mutually agreed to part ways and are proud of the series we made together”.
The deal with Spotify was reportedly worth $20million ($15.6million).
Under the terms of the deal, signed in 2020, Harry and Meghan was supposed to produce and host “programming that uplifts and entertains audiences around the world”.
The first of these projects was Archetypes, a 12-part podcast series hosted by Meghan.
The show included a list of star-studded interviewees such as Serena Williams, Mariah Carey, Constance Wu, Paris Hilton, and Mindy Kaling.