The website said Ms Markle had tried calling him on Monday and sent him a text saying she loved him and was concerned about his health.
The American TV actress' family has been in the news for their controversial statements about the bride-to-be.
He added: "Of course I'd walk her down the aisle".
May 12: The Daily Mail reports that viral photos of Thomas prepping for the wedding are fake.
One of the charities chosen by the royal couple is The Children's HIV Association, honouring a cause that was close to Diana's heart on their wedding day.
BA also said any passengers named Harry, Meghan or Megan flying on Saturday will be allowed to use its first-class lounge and all customers on the day will be given lemon and elderflower Victoria sponges, the same flavour as the royal couple's wedding cake.
It prompted Kensington Palace to respond that it was a "deeply personal moment" for Meghan, and that "she and Prince Harry ask again for understanding and respect to be extended to Mr Markle in this hard situation". Prince Harry and Meghan Markle on Monday night issued a statement asking for "understanding and respect" for Thomas Markle. After announcing earlier this week that he would not attend the royal wedding to walk his daughter down the aisle, he's revealing that he wants to head to London to be their for his daughter after all.
"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".
Meanwhile, Ms. Meghan's extended family has begun arriving in the United Kingdom despite not being on the guest list.
Markle does speak to her father, the retired lighting technician Thomas Markle.
Harry and Markle have invited 600 guests to the wedding, which will be followed by a gala reception hosted by the queen.
Kensington Palace, Harry's office, could not immediately be reached for comment on Tuesday.
"They [doctors] will go in and clear blockage, fix damage and put a stent where it is needed", Thomas told TMZ.
But he later said doctors had scheduled surgery on Wednesday morning.
"I think she would be over the moon, jumping up and down, you know so excited for me, but then, as I said, would have probably been best friends with Meghan".
Dooley and her sons, who live in OR, previously said they had not seen Markle in 20 years and had not received an invitation to the royal wedding. Maybe they wouldn't give her the time off to go to the U.K.so she bailed?
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