Biden said for him to meet with Kim there would have to be a commitment from the North Korean leader "that there's discussion about his nuclear arsenal."
"I would not do what had been done in the recent past; I would not give him all he's looking for - international recognition as legitimate and allow him to move in the direction of appearing to be more ... serious about what he wasn't at all serious about," he said.
Biden's comments appeared to reflect a shift in his thinking about a meeting. The White House had said in March it was not Biden's intention to meet with Kim.
U.S. officials have said only that Biden's policy would not be the approach favored by President Barack Obama of refusing to engage the North, and not Trump's flashy summitry.
At a joint news conference on Friday, Biden and South Korean President Moon Jae-in both said the complete denuclearization of the Korean peninsula is their goal. Biden said he was "under no illusions" about the difficulty of getting North Korea to give up its nuclear arsenals after his predecessors failed.