"It may not be very soon but it will be."
Vine replied, "That is the first time I have ever heard anyone say that."
Turner claimed that she "had it on fairly good authority" that Meghan 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."
It comes after Meghan's speech during Girl Up's Women in Leadership summit, in which she encouraged young women to take inspiration from world leaders like New Zealand's prime minister Jacinda Ardern.
"Another thing about those lawmakers, leaders and executives that I mentioned earlier - many of them better or worse do not listen until they have to," Meghan said.
"Because the status quo is easy to excuse and hard to break but it will pull tightest right before snapping.
"Women have always historically got a lot of 'that is not how it is done or that is an idea but we are going to do this instead' but when do we hear that as women?
"We hear that in the moments when we challenged the norms."
Some saw the speech as connected to her and Prince Harry's decision to leave royal life earlier this year. They now live in LA with their baby son Archie.
Daily Star Online has approached Meghan's representatives for a response.
