However, ending England's 60 years of hurt would send him into another stratosphere, all-but guaranteeing that he will get his hands on a prestigious Golden Ball, with the ceremony perhaps fatefully moved to London in honour of the great Sir Stanley Matthews, who was the inaugural winner 70 years ago.
As usual, though, Kane is keeping a level head despite the fact that immortality may beckon.
"I'd probably say I'll be up there for sure," he told L'Equipe recently when asked about his chances of Ballon d'Or success. "With the season I've had, I think with winning the three trophies, the numbers I've reached, I think I'll be in that conversation. If I win the World Cup on top of that, you would imagine it would be one of the England players.
"When you look at some of the past winners of the Ballon d'Or, for sure it comes down to the big games, the big tournaments, and you add that on top of what I've achieved this year, I think I'll be up there.
"I think you're starting to hear the noise about the players who are maybe favourites for the Ballon d'Or at the moment, maybe me and Michael [Olise] and some of the players who were Champions League finalists. So it's been an incredible season. I'm not the type of guy who wants to say I deserve the Ballon d'Or. I try and do my talking on the pitch."