Mr Markle, 77, had been planning to fly to the UK in June for the Queen’s platinum jubilee, with hopes to meet members of the royal family and his grandchildren – Archie and Lilibet – for the first time.
But on Tuesday morning he was rushed to hospital after having a stroke.
Karl Larsen, who has a YouTube channel with Mr Markle, confirmed the news to the PA news agency.
Mr Larsen said the retired director of photography had been looking forward to travelling to the UK for the jubilee.
Mr Markle did not attend Prince Harry and Meghan’s wedding in 2018 as he was recovering from heart surgery.
The news, first reported in MailOnline by Dan Wootton, comes after Mr Markle spoke last month of his desire to travel to the UK for the jubilee.
“I’m looking forward to it," Mr Markle told GB News from his home in Rosarito, Mexico.
“I’m going to show my respect for the queen and I’m going to make sure that the queen understands that my entire family respects the queen and the royals.
“We admire them and we want them to know that’s how we feel about them and that’s how we feel about England.”
He said he felt he had a right to meet his grandchildren.
Meghan has been estranged from her father since he was caught staging paparazzi photographs before her wedding.
He has said he hoped to face the duke and duchess in court as part of a defamation case being brought by her half-sister.