Tottenham have not mandated him to sign a new contract for now. Maybe they aim to keep him for one more season because he will be useful for them to compete for the league trophy or secure a champion league slot. But if the club wants to consider the business part of the deal, the best option will be to make him extend his contract or sell him this season. Besides these two options, Tottenham will lose close to €100m if they let him leave for free next season.
It seems that now the Harry Kane rumors are dragging on, we can see that it has been three seasons that Manchester United have not received the green light from Tottenham. If indeed Tottenham's goal is to maintain it to win a trophy then there is no reason for Postecoglou to fail again next season, at least being able to finish in the top five of the standings is very good. He has one year left on his contract, and if management feel they cannot maximize their form for next season's competition then I think it would be better to take the option to sell him. Because we know some other clubs really want him and maybe they will agree to the £100 million price clause that has been set. It seems that Tottenham will have to consider this soon before they lose Kane to a free agent when his contract expires.