Meghan’s aides have made clear that if he is willing to share a different address, it will be forwarded.
The pair have not been in touch since 2018, after the fallout over staged paparazzi photographs before the Sussexes’ wedding.
Markle made the comments from his hospital bed in the Philippines.
A surgeon responsible for his care told the newspaper that the procedure to amputate his foot was a matter of “life and death”.
“We had to remove the foot. There was a massive blood clot in his thigh and that had stopped circulation to his foot and lower leg,” he said.
“It was life-or-death surgery. Had the infection in the foot moved to his heart, it would most likely have been fatal. He is doing well but he is not out of the woods yet.”
As reports of her father’s ill health emerged, the duchess is said to have instructed aides to find out if they were correct before then contacting him by email.
Her spokesman said: “I can confirm she has reached out to her father”.
Markle was said to be fighting for his life after collapsing at his home in Cebu, in the Philippines, where he moved at the beginning of this year.
He underwent emergency surgery followed by a second operation to remove a blood clot, which was said to have resulted in his leg being amputated below the knee.
Markle suffered two heart attacks on the eve of his daughter’s wedding in 2018, which prevented him from flying to the UK. In his absence, the King, then Prince of Wales, gave Meghan away.
Markle is also said to have suffered a stroke in 2022.
The duke has never spoken to his father-in-law and Markle has never met his grandchildren, Prince Archie, 6, and Princess Lilibet, 4.
Prince Harry wrote in his memoir, Spare, that the duchess was “mourning the loss of her father”.
But Markle retaliated, telling an Australian television programme: “She killed me and then mourned me,” adding: “I refuse to be buried by her.”
In early May 2018, shortly before his daughter’s wedding, Markle, a retired television lighting director, made global headlines when it emerged he had colluded with a photographer to sell staged paparazzi shots of his preparations.
Despite the scandal, his invitation to the Windsor ceremony was not withdrawn.
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