According to the TMZ report, Markle decided not to walk his daughter down the aisle on Saturday, after it was revealed he worked with a picture agency to stage some pictures of him preparing himself for the wedding.
Thomas Markle said he now thought the pictures were "stupid and hammy," according to the TMZ report. He said he made the decision to skip the wedding so he wouldn't embarrass the royal family or his daughter.
CNN has reached out to Thomas Markle for comment over phone and over email but has yet to receive an answer.
CNN has learned that Prince Harry and Meghan Markle are very concerned about the pressure Thomas Markle is under and want the media to give him some space. CNN has also learned that though Markle is upset about what has transpired, her feelings about having her father give her away on Saturday haven't changed since photographs were published.
"This is a deeply personal moment for Ms. Markle in the days before her wedding," a Kensington Palace spokesman said Monday. "She and Prince Harry ask again for understanding and respect to be extended to Mr. Markle in this difficult situation."
Thomas Markle has been the subject of many unflattering media reports in the British tabloids as his daughter Meghan prepares to marry Prince Harry on Saturday.
Images of him at an internet cafe checking out a website featuring his soon-to-be royal daughter sparked an "awww" moment on social media last week.
But Markle's half-sister told a British TV network on Monday that she urged their father to stage positive photos for the paparazzi to help improve his image.
"I said the world has no idea that you're getting in shape and doing healthy things," Samantha Markle said on the ITV program "Loose Women."
"They don't photograph you buying vegetables and pH water, they photograph you in as (many) unflattering ways as they can. I said, 'Really you need to show the world you are getting in shape and doing great, healthy things.' So I suggested it."
In Sunday editions and online, Britain's Daily Mail published what it said was security camera footage showing Thomas Markle arriving at the internet cafe with a photographer.
Samantha Markle took full responsibility for arranging the photos, saying she was "entirely the culprit." When asked if her father had been paid, she said she didn't think so but wasn't sure.
"I do not believe so. That was not the motive -- it was my suggestion," she said. "I have no idea. But if he did, I am going to assume it was a pittance -- they don't pay that much. It really was so the world could see him doing the healthy things."
Meghan Markle, 36, has captured international attention as she prepares to become the newest member Britain's royal family.
The biracial American actress, like her fiance Prince Harry, is a child of divorce. Thomas Markle and her mother, Doria Ragland, met at a Hollywood studio in the late 1970s where he was working as a lighting director and she was a temp.
Her parents split when Meghan was young, but she told Vanity Fair this year that they remain on good terms and even take vacations together as a family. Earlier this month, Kensington Palace announced that Thomas Markle was scheduled to walk Meghan down the aisle at her wedding.
In her ITV interview, Samantha Markle accused the media of taking advantage of Thomas Markle, noting that their father, who is 73 years old, is "a bit more fragile."
"I feel that the media have unfairly preyed on him and he has really been admirable about laying low and not speaking out on certain things," Markle told ITV. "I merely wanted him to be seen in a respectable light and that wasn't being done."