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Biden cited Trump's 'erratic behaviour unrelated to the insurrection' - a reference to the riots at the Capitol Building on 6 January - as the reasoning behind his beliefs on the issue.
Speaking to CBS Evening News, the 46th President of the United States of America told Norah O'Donnell that he doesn't think Trump should receive the briefings.
When asked directly, Biden responded: "I think not."
He said he'd 'rather not speculate out loud', when asked what could possibly happen if Trump continued to get the classified information, adding: "I just think that there is no need for him to have the intelligence briefings.
"What value is giving him an intelligence briefing? What impact does he have at all, other than the fact he might slip and say something?"
However, despite the new president's comments, it doesn't seem as if anything has changed - for now, at least.
White House press secretary Jen Psaki said on Saturday: "The President was expressing his concern about former President Trump receiving access to sensitive intelligence, but he also has deep trust in his own intelligence team to make a determination about how to provide intelligence information if at any point the former President Trump requests a briefing."
It's been a longstanding tradition that former presidents can request and receive intelligence briefings, should they so desire.
I guess once you've been in charge of the USA and had your hand on the button, you know the importance of keeping that sort of stuff quiet, but might want to be clued in regardless.
It's not a given, though. The intelligence agencies have to review and approve any requests that they receive.
Psaki added: "The intelligence community supports requests for intelligence briefings by former presidents and will review any incoming requests, as they always have."
Another administration official recently told CNN that Trump has not submitted any requests to date, and it was an open secret during his own presidency that he'd often fail to read daily presidential briefings, according to reports.
Instead, Trump preferred to be brought up to speed verbally two or three times each week by intelligence officers, and presumably they'd have told him if there was anything serious that he needed to know.
In the same interview, Biden also refused to be drawn on whether he'd vote to impeach Trump were he in the senate.
Biden responded: "Look, 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.
"But I'm not in the Senate now. I'll let the Senate make that decision."
In earlier remarks, he said: "I've been saying for now, well, over a year, [Trump's] not fit to serve.
"He's one of the most incompetent presidents in the history of the United States of America."