The England striker has been in sensational shape this month, netting 9 targets in simply 5 video games.
Former Spurs boss Tim Sherwood lately recommended Kane would leave the membership in the event that they fail to win a significant trophy this season.
But Redknapp, who controlled the membership between 2008 and 2012, believes Kane has the entirety he wishes at Tottenham.
“He’s come from the youth team, at a great club, great training ground, with a great stadium when the new one is done.”
Last December, Kane signed a brand new handle Tottenham reported to be price £90,000-per-week – plus up to £30,000 in bonuses – till the summer time of 2022.
“The fans adore him, he’s earning fantastic money, he’ll go on to earn bigger money than he’s on now in the future,” Redknapp added.
“I might like to see him keep there longer term. He’s old skool, and old skool supposed you went to a soccer membership as a child and also you by no means thought of leaving.
“That used to be your membership. It’s modified now however Harry Kane is old skool so I believe he will know when he is smartly off and keep at Tottenham.”
Redknapp believes his previous membership have dented their identify credentials by way of opting for to spend a season enjoying at 90,000 capability Wembley, whilst their White Hart Lane house is torn down and rebuilt.
“I have performed Champions League with Tottenham, house merit used to be huge,” Redknapp mentioned.
“Teams got here to White Hart Lane and so they have been scared to dying. We completely smashed everyone up. They could not take care of it.
“Going to Wembley, giant open areas, slower pitch, it is a other sport.
But going ahead it is a nice Tottenham crew, I like the executive, and I believe it is a crew that if they’d performed at White Hart Lane this 12 months they’d were my tip for the Premier League.”