In comments that will be sure to trigger intense controversy among Republicans and Mr Trump's supporters, Mr Biden said there was no benefit to him receiving them, and that he may even let "slip" classified or sensitive information.
In an interview with CBS News, due to be broadcast over the weekend, Mr Biden said he would “rather not speculate out loud”, when asked what he feared could happen if Mr Trump continued to receive the briefings.
“I just think that there is no need for him to have the intelligence briefings. What value is giving him an intelligence briefing?”
He added: “What impact does he have at all, other than the fact he might slip and say something?”
Former presidents have tended to retain as a matter of courtesy access to high-level briefings if they request one. CNN said Mr Trump was not believed to have asked for one.
It said such briefings could be made in a number of ways, and the intelligence community would help put together any material that was presented.
The comments from Mr Biden came as the president again dodged a question on whether he would vote to impeach his predecessor, were he still a member of the Senate.
Having been impeached twice by the House - the only US president to be censured that way, the upper chamber is to next week begin its trial of the charge against Mr Trump.
No president has ever been convicted by the Senate, and if he was, Mr Trump could be banned from running from office again. As it currently stands, most observers believe Democrats will not win over enough Republican senators to secure the 67 votes they would require to convict him.
“I ran like hell to defeat him because I thought he was unfit to be president. I've watched what everybody else watched, what happened when that crew invaded the United States' Congress,” said Mr Biden, when pressed about how he would vote.
“But I'm not in the Senate now. I'll let the Senate make that decision.”
Mr Biden’s comment that providing Mr Trump with sensitive information could carry a risk, may ring true with those who remember the 2017 controversy over a meeting then President Trump had with Russian foreign minister Sergei Lavrov and Russian ambassador, Sergei Kislyak.
It was later reported that during the meeting at the Oval Office, Mr Trump had mentioned information about an upcoming operation planned by Isis, that had been passed to the US, apparently from Israel. It revealed Israel had a source inside the extremist organisation.
The White House denied any classified information had been shared and Mr Trump said he had “the absolute right to do”.
Earlier this week, White House press secretary Jen Psaki told reporters that “the intelligence community supports requests for intelligence briefings by former presidents and will review any incoming requests, as they always have”.
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