In an interview with Fox Sports Radio, Mr Trump said: “I would be inclined to go a different route than what he’s done.”
He said Mr Biden had “roped himself off into, you know, a certain group of people”.
Mr Biden is expected to announce his running mate in the coming days ahead of next week’s Democratic National Convention.
The United States has never had a female vice president, and the move comes four years after Hillary Clinton, the country’s first female presidential nominee, lost her White House bid.
Of Mr Biden’s vow to choose a woman, Mr Trump said: “Some people would say that men are insulted by that. And some people would say it’s fine.”
Biden campaign spokesman Andrew Bates said Mr Trump is “easily threatened”.
In a statement, Mr Bates said: “And because of his insulting negligence and erratic, failed leadership, over 5 million Americans have been infected with coronavirus, over 160,000 died, and tens of millions remain jobless.”
