Kane was on the scoresheet as Tottenham beat Aston Villa 2-0 on Sunday and they are now just three points behind Nevin’s former club Chelsea, who are sitting in fourth in the league table.
It has been suggested that the 27-year-old could consider leaving Tottenham, though would not be keen to damage his relationship with the fans.
Spurs chairman Daniel Levy is said to be not willing to sell him until a club offer him a minimum £120m.
Nevin admits that the rumours are terrible for Spurs, but he feels Tottenham fans would take it in their stride if Kane wants to leave.
He believes the striker has reached an age where it is now or never for him if he wants to compete for the biggest trophies in football.
Nevin said on Off the Ball: “It is not good for Spurs, but the other side is that they have had him for a long time and he has done a brilliant job.
“The reality is that Spurs fans can’t complain.
“They would be upset about it but they would absolutely understand it.
“You only get one career.
“He is 28 now? I mean he is at that age where this is it the last chance of making the big move, where you could have three or four years at a really top club.”
Kane has scored a staggering 215 goals for Tottenham in 327 appearances, but is yet to win a trophy in his career.
