The palace refused to confirm whether her father would be attending the wedding on Saturday.
A Palace spokesman said: "This is a deeply personal moment for Ms. Markle in the days before her wedding".
The Desert Island Discs host, who worked on a BBC documentary about the couple shortly after they announced their engagement, said they are a couple "very much in love".
Photos showed Meghan's Tracy Dooley - the ex-wife of Meghan's half-brother Thomas Markle Jr - and her sons, Tyler and Thomas, arriving at Heathrow Airport on Monday. Originally, he was supposed to walk Prince Harry's bride down the aisle.
But he appears determined to make his daughter's big day and told TMZ if doctors discharge him from hospital he will travel to England.
The last-minute decision to pull out was partly because of the fallout of reports that he staged paparazzi photos of himself, according to TMZ, and he also claims he suffered a heart attack six days ago. He is divorced from Meghan Markle's mother, Doria Ragland.
Doctors "will go in and clear blockage, fix damage and put a stent where it is needed", the 73-year-old was quoted as telling TMZ, which said Markle realized it was all but impossible he would be able to walk his daughter down the aisle.
As Grant noted, it wasn't known if Thomas Markle was paid for collaborating with paparazzi, but the pictures reportedly sold for $100,000. "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", she tweeted on her private account Monday. "Really, it's quite atrocious and intrusive and I think it's highly unethical".
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. What more fitting tribute to his mother than for Harry and Meghan to extend a warm welcome to 2,640 members of the public to celebrate their joyous occasion in the grounds of Windsor Castle?
"Actually she has a large family who were always there with her and for her", Ms Grant responded on Twitter.