Kane cast doubt on his Spurs future in a recent Q&A session amid rumoured interest from Manchester United and Real Madrid.
Tottenham are reluctant to lose their leading marksman, but a bid of £150m - plus pressure from the England international - may be enough for a deal to go through.
Should that be the case, Robinson wants lessons to be learned from seven years ago when his former club wasted the money from Bale's £85m sale to Madrid on a string of flops.
"It is difficult when a player of that magnitude and that quality says that they want to leave a club - it's just like with Gareth Bale," he told The Express.
"The deal has to be right. In the past, Spurs chairman Daniel Levy has made sure the deals are right and he has got excellent value for players.
"The deal would have to be right for everybody and it would have to be a very large sum of money that could be reinvested into the squad.
"The squad needs strengthening. To take Harry out of the equation you would need to reinvest the money very sensibly. You only have to look at Bale."