Di Canio took charge at Sunderland just two days after United won 1-0 at the Stadium of Light in late March and Ferguson's imminent retirement has denied the Italian the chance to pit his wits against the 71-year-old.
Ferguson was a fan of Di Canio during his playing career and was keen to bring him to Old Trafford in the early 2000s when he was at West Ham United.
"He called me two Christmas Days in a row and I thought it was my friend so I swore down the phone," said Di Canio. "He said 'no Paolo, this is Alex', I said 'Alex who? Is this you?' still thinking it was my friend and swore again.
"I said no, it was incredible to think about for me especially as I was 31 and he wanted me to play behind the strikers because Teddy Sheringham was nearly 40 and ready to quit. I thought this is mad that he wants me. I thought it was a joke but I said I can't trade.
"But it was a fantastic moment and gave me more energy because he was an important manager and you think you are a top footballer, I didn't have high esteem.
"I'm sad because we all know every story has to end one day. But I know in his book, he had three big regrets and one was not signing Paolo Di Canio. It made me proud.
"For the rest of my career as a manager, my big regret is not to be able to stand in the dugout next to him. It would be great to stand next to that football god.
"I saw all the documentaries and there is one moment which tells you why he won everything.
"On May 11 1983, he won a Cup Winners' Cup and after 10 days, he won the Scottish Cup and at the end of the day, his face was very angry and described it as a 'rubbish performance'. That is why he won everything; two cups in 10 days, but he was angry with his squad."
David Moyes has been confirmed as Ferguson's replacement and Di Canio feels the Everton manager deserves a crack at a big job.
He added: "David Moyes has proved he deserves to go one step forward to the top level. In my opinion, he is the right man.
"David has done an amazing job in the last 12 years at Everton. He has his philosophy and doesn't spend a lot of money.
"Good luck to him, it's a tough job, but we live to do these tough jobs."