The English international's form has allegedly made him a target for Los Blancos, but Redknapp has said that Kane could replicate former Liverpool midfielder Steven Gerrard in being a one-club player.
"I personally see Harry staying at Tottenham long-term," the former coach told talkSPORT. "If you mention most players I'd say yeah, they're going to want to go and win things and their agent is probably going to move them on, but I don't think Harry is one of those players.
"If there is a footballer in the county who wants to be loyal to his club, it would be Harry Kane. The boy is a one-off, he's unique, he's not your average modern footballer. He's a family man and he has a good life at Tottenham.
"It's like Steven Gerrard at Liverpool – we haven't seen that for a long time. Someone who is idolised by the fans and is part of the make-up of the club. I think that's what Harry is at Tottenham and I think that connection will only get stronger."
Tottenham are next in action on Tuesday when they face Juventus in the last 16 of the Champions League.