"I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle", Mr Markle told TMZ.
A likely candidate for the job could come in the form of Markle's future brother-in-law, Prince William.
He had been expected to walk his daughter down the aisle when she marries Prince Harry on May 19.
The gossip portal earlier reported that Thomas Markle, who lives in Mexico, was back in hospital with doctors warning his heart was "seriously damaged" after a heart attack a week ago.
The actress and activist has always been outspoken about her independence and it could be a telling gesture to walk herself down the aisle as she prepares to join the world's most famous family. They were due to travel to the chapel together on Saturday.
Asteroid 2010 WC9 to pass between Earth and Moon tomorrow
Now, imagine the damage that could be done by an asteroid the size of a house entering the atmosphere at more than 45,000 km/h. Even if the actual size of the 2010 WC9 was close to the maximum estimate, the space rock did not pose a threat to humanity.
Guests will arrive at St. George's Chapel at Windsor Castle between 3:30 a.m. and 5 a.m.
On Monday, Ms Markle's half-sister Samantha admitted involvement in faking the photos, but insisted it wasn't motivated by money.
He said he had agreed to the pictures because he hoped they would improve his image, as previous paparazzi snaps had shown him buying beer and looking dishevelled, TMZ said.
Along with the royal attendants, the palace announced eight other youngsters picked by the couple for a special role in the wedding ceremony.
Mr Markle told TMZ he changed his mind after his daughter contacted him to say she loved him and was concerned about his health.
Ms Markle's goddaughters, Remi Litt, six, and her elder sister, Rylan, seven, will also be joining the procession of bridesmaids.