While Kane is regarded as a club legend, the forward has acknowledged that he will consider his options should the North London outfit not win any silverware in the short term.
Redknapp has backed the stance of the 26-year-old, who he has acknowledged may have ambitions away from the Premier League side.
Speaking to Sky Sports News, Redknapp said: "Listen, Harry is an ambitious boy. He's a fantastic professional, a great lad, and he wants to play and he wants to win things.
"[Tottenham] need surgery in the summer, but are they going to be spending any money? Is anyone going to be spending money now in the next year or two and going for big transfers? He'll be looking at that and thinking 'hang on'."
Kane has scored 181 goals from 278 appearances for Spurs in all competitions.