So the story goes, Levy - while reluctant - isn't shutting the door on cashing in on Kane this summer. With Manchester United and Manchester City among those monitoring developments, it's claimed Levy would consider selling for £150m.
Really? Really? Still with over three years to run on his contract. A Carabao Cup final to look forward to. Alive in the FA Cup and Europa League. And as Jose Mourinho, his manager, said just Tuesday, no-one inside the dressing room is giving up on a top four finish this season. Okay, okay, they've had their stumbles - and ninth place on the table doesn't look good on paper. But win their game in hand and Spurs are three points outside the top four. This isn't a team on the slide. It certainly isn't a team in crisis.
Indeed, you just wonder what Kane is making of it all this morning. This one was out of the blue. There's been no real soundings from anyone connected to the Kane camp about him being unsettled. Indeed, it's the opposite. Confirmation arriving just yesterday that Kane is amongst the most loyal of Spurs players towards his manager.
Could the source of these claims be coming from higher up? Levy? Or even Joe Lewis, the club's prime financial backer? In football - in this industry - you can't rule anything out. But you do fancy Levy and Lewis are a bit brighter than this.
As we've noted in a previous column, in terms of the personalities now working at Spurs Lodge, the top brass must know they're sitting on a marketing goldmine. Mourinho, Heung-min Son and Kane. They're a marketing team's dream. And the idea that £150m for a 27 year-old Kane would be good business for Spurs is ridiculous. Maybe on the pitch. Maybe what he can offer another manager in another team. Sure. But overall? If Levy were to sell at such a figure this summer, he might as well shut the doors.
Mourinho and Kane on the same page
Over the next 18 months, as England captain, no player in the country, potentially no player in the world, is going to generate as much media interest as Kane. The Euros this summer. The World Cup a year later. If ever Kane's profile is to break beyond football circles it will be over the next year. And he should being do it as a Tottenham player.
Kane isn't Luka Modric. Nor Gareth Bale. He's happy where he is. He's happy with his manager. And even if a Manchester United or Real Madrid were to come in for him, there's no way he'd emulate what Modric and Bale did in terms of downing tools and forcing a move away. The deck really is stacked in Levy's favour.
Of course, the link with the new stadium is an obvious one. The lockout. The need for repayments. It's a story that does bear credence. But again, like with Kane and his minders, there's never been anything from Levy about the concern of meeting stadium costs. That he green lit deals over the summer for the likes of Pierre-Emile Hojbjerg, Sergio Reguilon and Matt Doherty, spending over £65m in total, doesn't suggest there's a worry about covering the stadium's outlay.
So the player is happy. The board are calm. And the team has everything to play for. Go a step further and those signings Mourinho has brought to the club have all proved value for money. No-one, not een the most avid anti-Mourinho pundit, could claim Hojbjerg and Reguilon haven't bettered their price-tag. So just where on earth does such a story come from?
Well, for this column, it's the new status of Spurs under Mourinho. Levy going with the Special One catapulted the club to a new level. As big as Spurs are, they're now a daily headline driver with Mourinho as manager. 50 per cent love him. 50 per cent hate him. But 100 per cent of the media want to talk about him. And it's this which is driving the sack talk - as it is with the Kane transfer claims.
Again, take a step back. Look at what Spurs have to play for this season. And it's clear Mourinho shouldn't be under any type pressure in his first full season in charge. Of course, Spurs could be doing better - and he's the first to admit this. But this is no disaster campaign. If those players on the fringes... the ones who are pushing all this chatter about a divided dressing room... if they can't get excited about their prospects in the final stretch of the season, then they're only proving Mourinho's right to blank them. Which you hope is the same approach the club and Kane give to this story.
Sitting in mid-table. One win in the Prem from the last five. As a headline, it makes sorry reading. But you don't have to scratch away too much to see the potential of this team, this club and what is well within it's reach.
And beyond Mourinho, right at forefront has to be Kane. This story about Levy and a willingness to sell, surely it has no legs to it...?