Why wouldn't he have signed a new contract already, though? It doesn't really make much sense as he would know any new contract will sign away the rest of his career, so he would have accepted that by now. I also cannot believe this is the first time he would have been offered a renewal after what happened with Man City, so he has likely put it off, or turned it down, beforehand.
Tottenham would likely be willing to pay almost anything he wants, so money would not be an issue. So what would the hold up on a new contract be?
The only reason that makes sense is extreme doubt in Tottenham, which would have been reinforced by their terrible league season. So, what could possibly sway him into signing a new contract for Tottenham? We have to remember he already showed doubt in Tottenham when he clearly wanted to leave for City.
Even if they keep him next season, they would literally have to challenge for the Premier League title to have any chance of changing his mind. Nothing else would be enough.
If Kane were to sign a new contract, I believe he would have done it already.