According to The Sun, Meghan's half-brother, Thomas Markle Jr, alleged he found a stash of images belonging to their father at his former home in the Philippines.
He reportedly told police in the country he discovered the child abuse pictures and videos mixed up with innocent family mementos.
The newspaper said he also contacted FBI investigators in the US in July.
Authorities in the Philippines said they are investigating the allegations.
In an interview with the Mail on Sunday, Thomas Markle Sr said he has "never had sex with anyone under the age of 18".
He said when he was single he travelled to the Philippines at least twice and "slept with prostitutes".
"I like Asian women but that is not a crime," he said.
"I am not well enough to go to the Philippines but I will speak to anyone who wants to talk to me. I have nothing to hide."
Thomas Markle Sr is learning to walk again at a nursing facility in Florida after he had his leg amputated during life-saving surgery in 2025.
He said he would also welcome any forensic examination of his computer.
"If there is anything bad on there it was put there by someone else," he told the Mail on Sunday.
His eldest daughter Samantha Markle defended her father, telling the paper: "I believe this is a set-up".
It comes after the Metropolitan Police on Saturday confirmed it passed a letter with claims of alleged offending outside the UK by Thomas Markle Sr to Meghan and Prince Harry but did not share details with other law enforcement agencies.
The force said it received a letter in 2019 about a "number of claims" relating to Thomas Markle Sr, adding it was "reviewing the handling of this matter", including whether the force needs to be referred to the police watchdog.
On Friday, Meghan said she was made aware of "disturbing allegations" about her father in 2018.
She said she was shown a letter sent to Scotland Yard eight years ago making "troubling" allegations against her father and was assured they were being investigated.
A spokesperson for Meghan said if police had a time-stamped record confirming the letter was reviewed in 2019, then that "should be treated as the accurate reference point for when it was received and shared with the Duchess".
It was "understandable" because of the passage of time that Meghan "may have been mistaken by a few months", they said.
According to The Sun, Meghan sent a letter to her father in 2025 which reportedly said she knew of the accusations against him and that she would never allow him to meet his grandchildren.
Meghan became estranged from her father in the run-up to her 2018 royal wedding after he was caught staging paparazzi photographs.
He did not attend the wedding, leaving the King to walk Meghan down the aisle.
Thomas Markle Sr moved to the Philippines in 2025 after suffering a series of strokes.
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