Thomas Markle had told TMZ he would not go amid a row over paparazzi photographs; then that he would; then that he could not, due to a planned heart procedure.
Kensington Palace declined to comment.
Meghan Markle’s estranged half-sister, Samantha, said he had faced an “unbelievable stress”.
Speaking to Australia’s Sunrise morning TV program from Orlando, Florida, Samantha Markle said she was not sure if Thomas Markle would be travelling to Windsor.
She said: “He sent me a message that he was undergoing heart surgery.
“We’re all hoping he pulls through this now.”
Thomas Markle became embroiled in controversy at the weekend, following reports that he staged paparazzi photographs of himself in the run-up to the wedding.
The pictures showed Thomas Markle – apparently unaware he was being photographed – in a series of wedding-related activities, including being measured for a wedding suit.
Samantha Markle, who has not spoken to her famous sibling in three years – and will not be attending the wedding – told Good Morning Britain the photographs had been done with “good intention” and not for money.
She previously admitted the pictures had been her idea, in order to portray a positive image.
On May 14, Thomas Markle reportedly told TMZ that he would not attend the wedding.
TMZ later reported that Meghan Markle’s father had and wanted to attend – although he might not be able to because of health concerns.
In a third report, TMZ said that the health issues and planned surgery would prevent him from attending after all.
Thomas Markle had been due to meet Prince Harry for the first time this week, as well as Queen Elizabeth and Prince Philip, before walking his daughter down the aisle at St George’s Chapel in Windsor Castle.
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