The news website also claimed that he had recently suffered a heart attack.
"I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle", he admitted.
It has to be said that others in Ms. Markle's family - particularly ancillary members who have not been invited to the wedding - have not helped.
The latest report adds to the wedding confusion caused by Mr Markle, who was quoted as saying Tuesday he would not attend the ceremony after a backlash over an alleged $180,000 payment he received for staging photographs with United Kingdom tabloid the Mail on Sunday.
Kensington Palace did not confirm whether Markle senior had pulled out of Saturday's wedding at St George's Chapel in the castle's grounds but issued the statement hinting all was not well.
9NEWS US Correspondent Charles Croucher spoke to a hospital in Rosario, Mexico, where Mr Markle was taken several days ago, and a spokesperson said he only spent one day there on May 3.
"He sent me a message that he was undergoing heart surgery", she said, "He's been under a tremendous amount of stress amidst health challenges". The father of the bride said, "This is a historic moment. Knowing that they really share the same values as I do about food provenance, sustainability, seasonality and most importantly flavor, makes this the most exciting event to be a part of".
Asked how he thinks the Queen will feel about the recent drama, Markle Sr joked she wasn't likely to be thinking about what he's doing.
Don't count out Thomas Markle just yet.
As disgusting as it is for Meghan to have her father ditch her only days before her wedding, this is an opportunity for Meghan to rock the establishment - again.
CNN has reached out to Thomas Markle for comment over phone and over email but has yet to receive an answer.
She also added the media had "raked him over the coals" and "distorted his image", stating that "he had a moral right to set the record straight and defend himself".
"The bottom line to me whether he took money [for the paparazzi photos] or not is did she have a close relationship with her father?"
A source told Britain's Express newspaper that "Her Majesty and the Duke are very angry with Meghan's father".
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