Di Canio has divulged details of a phone call he had with Ferguson in 2001 where he turned down the opportunity to join United.
"I thought it was a joke, I thought it was my friend from Italy," Di Canio told the Sky Sports News' Transfer Talk podcast.
"My stomach went a bit because it makes you think you have underestimated yourself, that you are bigger than what you thought. Man United call you, try to persuade you to move because they want you. For a couple of minutes you feel big and strong.
"It was strange for me to say no to Sir Alex. I said 'thanks, 1000 times thanks, but I can't. West Ham are the family that warmed to me in the worst moment in my life, I'm the skipper, I can't'.
"He told me, 'Paolo, respect for this, I love people that think in this way. You are the man that I thought you were'."
Di Canio to this day insists he has no regrets about his decision, saying he owed everything to West Ham.
"In the end I remained at West Ham and I don't have regrets about it, even if United became the best, won the Champions League, winning the leagues. I would never change winning those leagues for the four and a half years I wore the West Ham shirt."