Two towering figures of football's modern era, Maldini won seven Serie A titles and five European titles during a 25-year Milan career, while Ferguson's 13 Premier League crowns and two Champions League triumphs established United as a dominant force at home and abroad.
Speaking at the launch event for the International Champions Cup in New York, Ferguson spoke on stage alongside Maldini and said his father – former Italy boss Cesare – gave the prospect of the all-time great left-back moving to Old Trafford short shrift.
"I did try [to sign Maldini] but when I met his father he was quite formidable, I got a shake of the head," Ferguson explained in a light-hearted exchange.
"He said, 'My grandfather is Milan, my father is, I am Milan, my sons are Milan. Forget it'."
Ferguson bowed out having secured his final Premier League title at the end of the 2012-13 season and concedes to still missing the thrill of the big occasion.
"I must admit, I miss the big games – the cup finals. They are fantastic," he said.
"It turns inside your stomach for an hour before the game. When the players are out for their warm-up, you're on your own.
"You're looking for someone to talk to, you just can't wait for the game to start. The excitement is boiling up in you and I really miss that."
Ferguson helmed pre-season tours to the United States during his later years in charge and believes such occasions add an extra intensity to a side's preparations for the forthcoming campaign.
"Many years ago, our pre-season was probably done in a less intense way," he added. We'd go to Scandinavia and places like that for a gentle build-up until the matchdays started in the league.
"When we went to the States it became more serious.
"The difference is that we can't afford to lose to Barcelona or Real Madrid or Manchester City or Milan. The expectation is too big.
"That's why you always get the full product when Manchester United play in these games."