Alli was hot property two years ago for his performances at MK Dons and the dynamic midfielder opted to move to Tottenham.
The 20-year-old has gone onto establish himself as an England international and has scored seven league goals in his last five appearances.
But Redknapp was surprised Manchester United didn't try to snap up Alli after seeing first hand the midfielder's talents when MK Dons handed Louis van Gaal's side a shock 4-0 defeat.
Harry Redknapp believes Manchester United should have signed Dele Alli
Dele Alli has scored seven goals in his last six appearances
"I always look back at that MK Dons game. United should have had him on coach back to Old Trafford, he ran the game," Redknapp told Betsafe.
"Surely you'd have gone out and bought him."
But United's loss is certainly Tottenham's gain, according to Redknapp who believes he is the full package.
"I'm such a fan of his. He's got everything," he added. "He can head it, tackle, shoot, dribble, score goals.
"He's the full package. He's got a bit of an edge to him, I love watching him play, he's amazing."