"And this would be your President, possibly? I don't think so. I don't think so.
"You know, I want to see the first woman President also, but I don't want to see a woman president get into that position the way she'd do it, and she's not competent.
"They're all saying 'we want Ivanka'... I don't blame them," the President added.
Earlier this month, Harris made history by becoming the first Indian-American and African American to formally accept the nomination for the Democratic Party's Vice Presidential candidate.
Trump's remarks on Friday came a day after the California Senator said that the 2020 Republican National Convention (RNC) it was "designed to soothe his (Trump) ego".
In a speech on Thursday, Harris railed on Trump's handling of the coronavirus pandemic, saying that "you can't stop it with a tweet".
Trump has launched attacks against Harris since she was named to the Democratic ticket earlier this month, The Hill news report said.
He has regularly derided her as "nasty" and also entertained a false conspiracy theory about her eligibility for the vice presidency.
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