The presenter told Channel 5's Jeremy Vine that she had it on "good authority" that the Duchess of Sussex intends to run for office.
Meghan and Prince Harry moved back to the United States in January and have have been vocal on a number of political matters such as Black Lives Matter and climate change.
Ms Turner stated that she did not know when Meghan might make a bid for the White House - but it could be in the not too distant future, reports the Express.
America is set to go to the polls in November with Democratic presidential nominee Joe Biden looking increasingly likely that he will replace incumbent Donald Trump.
Ms Turner said: "She will run for President, I have no doubt about it.
"I have no doubt, I think this is all part of the plan. It may not be very soon but it will be."
A rather sceptical Jeremy Vine said it was the "first time I have ever heard anyone say that."
Ms Turner replied: "I have it on fairly good authority that she would like to run for President
"There may be worse Presidents, I would like to see a mixed-race woman in the White House, I would."
