The England skipper only has one year left on his deal with the north Londoners and is being pursued by both Bayern Munich and Paris Saint-Germain this summer.
German champions Bayern have already had two offers rejected for the 29-year-old, the second of which was worth £70million.
Spurs chairman Daniel Levy has no intention of letting Kane leave despite his precarious contract situation and it would take a far greater offer for that stance to change.
PSG are believed to be readying their own bid for the forward which could reach nine figures, though his preference is a move to Bavaria.
Kane is already believed to have verbally agreed terms with Bayern and met with Thomas Tuchel, who has convinced the striker they can win the Champions League together.
But Tottenham’s hierarchy still believe they can persuade Kane to remain at his boyhood club beyond 2024 and The Telegraph are reporting that they have restarted their charm offensive following his return to training.
Kane reported back for pre-season on Wednesday and Spurs have tabled a contract offer worth £400,000-a-week – a salary that would make him one of the highest-paid players in the Premier League.
In addition to that huge financial incentive to stay, Tottenham are looking at ways to keep Kane at the club after his playing career finishes.
They have helped nurture the coaching careers of former players like Ryan Mason and Jermain Defoe, while they could also give Kane an ambassadorial role if that is what he prefers – something similar to the job former captain Ledley King currently has.
Another option could be going down a sporting director route not dissimilarly to Mark Noble at West Ham, with Tottenham keen to keep all options on the table.
Kane has now held his first chat with new boss Ange Postecoglou and, according to football.london, the Australian coach left a positive early impression on the forward.
Although the meeting was far from any kind of transfer showdown, with Postecoglou keen simply to get to know his star player, both men got on well and Kane is believed to be impressed with what he has seen at training under the new regime since returning.
MORE : Paris Saint-Germain challenge Bayern Munich in race to sign Harry Kane from Tottenham
MORE : Ange Postecoglou reveals the only thing that would make him consider selling Harry Kane
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