While asking her question, the reporter said that the royal pair "essentially encouraged people to vote for [Democratic nominee] Joe Biden."
"I'm not a fan of hers," he said at the press conference. "And she probably has heard that. But I wish a lot of luck to Harry because he's going to need it."
The Hill published a clip video from the conference to Twitter.
The president has spoken publicly about Markle, 39, and Harry, 36, a number of times, including shortly after they announced that they would step away from their duties as senior members of the royal family.
"Well, I think, you know, I don't want to get into the whole thing," Trump said during an interview with "The Ingraham Angle" earlier this year. "But I find it, I just have such respect for the Queen. I don't think this should be happening to her."
Citing maternity leave, Markle also skipped out on a handful of events during Trump's state visit to the U.K. in June 2019.
Around the same time, a past video of Markle resurfaced in which she said she'd be voting for Hilary Clinton in the 2016 election, calling Trump "misogynistic."
Then, an interview with the president was published, in which he reportedly called Markle "nasty."
Trump has since denied using such language.
"I said she was nasty about me," the president had said. "And essentially I didn’t know she was nasty about me."
Meanwhile, on Tuesday, Markle and Harry spoke about the importance of voting during their segment of the broadcast celebrating Time magazine's most influential people of the year.
Harry is a citizen of the U.K. so he's ineligible to vote in the upcoming presidential election, told viewers that he hasn't "been able to vote in the U.K. my entire life," he said according to People magazine, because members of the royal family are restricted from doing so.
Harry continued: "As we approach this November, it’s vital that we reject hate speech, misinformation and online negativity."