Kensington Palace has not confirmed the accuracy of the report, and have not yet commented.
TMZ, the celebrity gossip website, quoted Mr Markle as saying he meant no harm to Ms Markle or Prince Harry after taking part in an arranged photoshoot with a paparazzi agency.
He allegedly claimed he had not made the decision because of money, but in order to recast his image after a series of unflattering photographs were taken.
"He's now decided not to go [to the wedding] because he doesn't want to embarrass the Royal Family or his daughter," TMZ reported.
Hours earlier, Meghan Markle's half-sister claimed responsibility for a setting up a controversial paparazzi photoshoot for her father.
Samantha Grant, who is no longer in contact with Ms Markle, said she had suggested their father pose for "positive" photographs "for the benefit of the Royal Family".
Instead, the images caused deep embarrassment, appearing to show Mr Markle colluding with photographers despite Kensington Palace's repeated insistence that he was a private individual who had no interest in working with the media.
Grant, writing on Twitter, said: "The bad press over my father doing staged photos is my fault.
"The media was unfairly making him look bad so I suggested he do positive photos for his benefit and the benefit of the royal family.
"We had no idea he would be taken advantage of. It was not for money."
It is not clear what Grant meant in her claim that he had been "taken advantage of".
Appearing on Loose Women on Monday, she elaborated to say that she was "entirely the culprit" in staging the photographs, convincing her father that it would be to his advantage to show himself in a positive light.
"It was my suggestion that to benefit him and to benefit the Royal Family and that everyone looked good, and they depict you as you are," she said.
Pressed on whether he had been paid for his cooperation, Grant said: "I have no idea but if he did I'm going to assume it was a pittance, because they don't pay that much.
"It was really so that the world could see him doing the healthy things that he's doing."
Asked about the effect on Kensington Palace, after aides repeatedly insisted Mr Markle did not wish to be photographed, she conceded: "I can understand why it would be awkward."
Her brother, also called Thomas, has said that Mr Markle "won't saying anything publicly but he'll apologise sincerely to Meg and the Royal Family".
Mr Markle has been receiving the support of Kensington Palace since news of Ms Markle's engagement brought him into the public eye, with a source saying aides would "continue to make interventions with the media out of concern for his safety and security".
Kensington Palace has previously issued warnings to the media not to publish pictures of Mr Markle or Ms Markles mother, Doria Ragland, taken under circumstances of harassment, insisting they had no wish to take part in any personal publicity.
But a series of photographs, printed in the tabloid press, aroused suspicion after showing Mr Markle exercising in public, reading a book called "Images of Britain", being measured for a suit, and looking up pictures of his daughter in an internet cafe.
This weekend, the Mail on Sunday published CCTV images appearance to show him collaborating with a photographer, walking into the cafe with him and setting up the best angle.
This article originally apperaed on the Daily Telegraph.
