Kane stayed this season despite the 28-year-old reportedly believing he had a verbal agreement with Levy to depart.
Speaking on Sky Sports, Redknapp seemingly confirmed the striker had an agreement to leave the club if a £130m bid came in.
He fumed: "I found that surprising this summer because every other time they've had a real asset, you think Modric, Bale, Carrick, Daniel Levy has decided to sell, took the money.
"The one time that they get an incredible amount of money, great offer to a player who obviously wants to leave, I think there was a verbal agreement £130million, they decide to say no.
"I didn't understand that, it didn't make any sense to me and I know you've got to keep your best players but I think they could've invested again."
Kane was strongly linked with a move to Manchester City in the summer but an initial £120million offer was rebuffed by Spurs.
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