The England international's stellar form in front of goal continued on Saturday afternoon as he netted another brace against Everton, helping Spurs to run out 4-0 winners at Wembley Stadium.
Kane's breathtaking 2017 has attracted rumoured interest from Real Madrid, but Redknapp believes that the 24-year-old - now Tottenham's record all-time scorer in the Premier League - will stay put.
"I don't see Harry Kane being a player who leaves Tottenham," he told talkSPORT. "I think he's happy there. If he gets a good contract and he's looked after I don't seem him chasing big dreams elsewhere.
"Tottenham beat Real Madrid this season in the Champions League. At Barcelona, with the players they have got there and the way they play [would he fit in]?
"Tottenham are a big club, they are in the top four or five clubs in this country so I would think he's quite happy. His life is probably fantastic at the moment."