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.
"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.
"He's the full package. He's got a bit of an edge to him, I love watching him play, he's amazing."