The Duchess, 39, is reportedly targeting the 2024 campaign, in case current President Joe Biden decides not to run for a second term.
Markle's biographer, Omid Scobie, has previously spoken about her political ambitions and how the former actress has "her eyes set on the US presidency".
"Meghan is the embodiment of the American dream. One day we may see Meghan become president," the author of "Finding Freedom: Harry, Meghan And The Making Of A Modern Royal Family" told a documentary.
In an interview with Vanity Fair last year, a friend of Markle's told the magazine she would "seriously consider running for president".
"One of the reasons she was so keen not to give up her American citizenship was so she had the option to go into politics," the friend said.
However, another one of Markle's biographers said the Duchess does not have the "skin of a rhino to run for office".
"I would state categorically that she has no chance of ever running for president. She would be eaten alive," the biographer, Andrew Morton, author of Meghan: A Hollywood Princess, has previously told Vanity Fair.