Growing speculation about Biden's plans were further fueled by reports over the weekend that he had met privately with Senator Elizabeth Warren, an influential voice in the Democratic Party's left wing.
Clinton's campaign, meanwhile, has been burdened by continuing controversy over her use of a private email server while secretary of state, a matter being looked into by the FBI.
"I think they're the same. I think that Hillary may be very damaged, however ... Because of the email thing," Trump told ABC's 'This Week' talk show when asked if Biden would be a tougher opponent than Clinton.
"But I don't know, assuming she could get over that, which I just don't know how she possibly can, but if assuming she could, I would say it would be pretty equal," he added.
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Clinton agreed to turn over her private server to the Federal Bureau of Investigation but has insisted she is confident she "never sent or received any information that was classified at the time it was sent and received."
David Petraeus, who was forced to resign as director of the CIA in 2012, was given two years' probation and fined USD 100,000 in April for providing classified secrets to his mistress.
Warren, who has an enthusiastic, loyal following among liberals in her party, has so far endorsed no one in the race.
Other Republicans vying for the presidency and appearing on Sunday talk shows joined Trump in attacking Clinton.
"Here's the problem with Hillary Clinton. Hillary Clinton won't answer any questions," New Jersey Governor Chris Christie said on CBS's "Face the Nation" show. "Why did she have a private email server to begin with? And why was she doing all of her business over a private email server?"
When the interviewer pointed out that Clinton's defense seemed similar to Christie's during "Bridgegate," he responded: "Yea, except that I'm telling the truth. And she's not."
Carly Fiorina, the only other woman in the race, told NBC's "Meet the Press" that she "absolutely" had admiration for Clinton, noting she had "dedicated herself to public service."
A poll last week showed that Trump is increasingly competitive in a general election matchup against Clinton, trailing the top Democratic contender by just six points.
The CNN/ORC poll showed Clinton leading Trump by 51 percent to 45 per cent, a dramatically tighter race than July's 56-40 spread and June's 59-35.