The England captain was heavily linked with a move away from Spurs during the summer, with Premier League champions Manchester City keen on acquiring his services.
Tottenham chairman Daniel Levy, though, maintained that Kane was not for sale and managed to keep hold of the centre-forward beyond the summer.
Manchester City are now rated as unlikely to return for Kane and attention has turned towards whether the striker will sign a new deal with Spurs.
Kane is claimed to have turned down a contract offer just days after the European Championship final, but will sign a new deal if Spurs agree to insert a release clause in the agreement.
Levy is not a fan of inserting release clauses into players’ contracts, but the 28-year-old is hopeful that he can be an exception.
Having been priced out of a move in the recently concluded transfer window, Kane is keen to avoid such a situation in the future and a release clause would let suitors know how much they have to pay for him.
A new deal for Kane would mean a huge pay rise, but the package would not be close to what he was expecting at Manchester City, who are claimed to have been willing to offer him as much as £500,000-a-week.