No it won't. Kane's value to Spurs is his goals, not his monetary value. If Spurs doesn't get what they need for him it is far more beneficial to keep him, add a bit of talent and go for a trophy/top4 finish. Spurs would need 2-3 quality players to replace Harry Kane this season, and if no one is willing to pay that, then why should they sell? Build the team up a bit more this season, try to get the most our of him, and splash the cash next season on a new striker when he leaves for a free anyway. Maybe an a academy product will be ready then, or a new talent will emerge. At 70M euros there is no benefit to Spurs.
Unless Spurs get enough to cover most of what they lose, they have no incentive to sell.