Biden told ABC News that he "would have been the best president" if he had run.
He decided against mounting a campaign following the death of his son last year.
"No one should ever seek the presidency unless they're able to devote their whole heart and soul and passion into just doing that," Biden said.
"And Beau (Biden) was my soul. I just wasn't ready to be able to do that. But, so, my one regret is Beau's not here. I don't have any other regrets," Biden said.