Ms Ragland was the only member of the bride's family to attend the royal wedding in May.
A close friend in Los Angeles told the news outlet: "She is getting ready to move to London. I think she will be going as soon as possible.
"I know that she was eager to live closer to her daughter."
Meghan, grew up in Windsor Hills, California, where her mother still lives in her childhood home.
In an interview he has claimed will be his last, Thomas Markle said his phone conversation with Duke of Sussex left him feeling upset since it happened while he was recovering in hospital from a heart attack.
Mr Markle sparked a media storm when he staged paparazzi pictures in the run-up to Meghan and Harry's wedding, including shots of him reading about the couple online in an internet cafe.
The retired lighting director, who later pulled out of attending the wedding after suffering a heart attack, has said since that he had apologised to the pair for taking part in the photos.