Speaking to MSNBC, Biden said he would never tell President Barack Obama "for certain" that he wouldn't accept a nomination for the panel. But he said he had "no desire to sit on the Supreme Court" and called for a "consensus candidate" that can gain approval from Republicans.
"I will be deeply involved" in the nomination process, Biden added later, saying he hadn't yet held a sit-down meeting with Obama to discuss the high-stakes appointment.
"It's one of my roles as vice president to be an interlocutor with the Senate and the House because everybody up there knows I respect them and I enjoy it. And I have a lot of good friends on both sides of the aisle up there."
Biden graduated from the law school at Syracuse University in 1968 but left near the bottom of his class. Facing allegations of plagiarism during his 1988 bid for the presidency, Biden released his law school records showing he graduated 76th out of 85 law students.
The plagiarism allegations arose as Biden oversaw the Senate Judiciary Committee hearings for President Ronald Reagan's nominee to the Supreme Court Robert Bork, who was ultimately rejected by lawmakers. But Biden said he met with Reagan to discuss the nomination process, despite coming from opposing parties.
Biden said Obama would assuredly meet with the current Senate Judiciary chairman, Republican Sen. Chuck Grassley, who has yet to say whether he'll convene hearings on Obama's eventual court pick.
"I'm confident he'll reach out to the Senate and go through the process of advise and consent," he said, noting the qualifications Obama was looking for would include selecting a "consensus candidate."
"The Senate does have a right to have a say in who, and what the philosophy of the nominee is. But they only get to dispose. The President proposes," he said.
Obama's process for selecting a replacement for Antonin Scalia, who died suddenly last weekend, it still in the beginning stages, the White House said Thursday. He's met with senior advisers to plot a path forward, and administration officials have been in touch with Republicans and Democrats on Capitol Hill.
But Obama has yet to convene a meeting at the White House with Senate leadership or Judiciary Committee members. The Senate Majority Leader Mitch McConnell said hours after Scalia's death Saturday that the next president, and not Obama, should name Scalia's replacement.
Biden speculated Thursday the move was rooted in pressure from the conservative wing of the GOP.
"I think because they're intimidated by the dominant element of the Republican Party, the national politics right now, the far right. I think they're intimidated by it. I think it's the tail wagging the dog," he said. "I think the leadership went out to make sure they got out ahead of Ted Cruz. I don't believe in their heart they think this makes sense."