Kane has made no secret of his desire to win silverware, though always said he would stay at Spurs if he felt that was possible.
It is understood that Kane has now run out of patience and has informed the club of his intention to leave.
With Spurs still looking for a new manager, this summer is shaping up to be the most important at the club in a generation.
Here's what we know so far...
Harry Kane has informed the club of his decision to leave and wants to remain in the Premier League.
Kane also reportedly wants clarity over a possible exit before the Euros, which start on June 11.
Standard Sport understands that Kane was last year persuaded to stay for another season, what was expected to be Jose Mourinho's first full season in charge, and try to win a trophy and chairman Daniel Levy shook on a transfer this summer if Kane’s view didn’t change.
Kane now hopes that the ‘gentleman’s agreement’ will be honoured and he will be allowed to leave.
Sky Sports News claim that Spurs are preparing for life without Kane and have started making enquiries over replacements.
Where would Kane go?
He continues to chase Alan Shearer's long-standing Premier League goal tally of 260 and, as he approaches his 28th birthday, time is on Kane’s side with 165 to his name
So, a move to a Premier League rival is most likely, though any move can still be considered unlikely given the strength of Tottenham’s hand.
Manchester United, Manchester City and Chelsea have all contacted Kane’s entourage to gauge his feelings.
United are not understood to be looking for a new striker after tying Edinson Cavani down for another season, though have held an interest in Kane dating back years.
Tensions remain at boardroom level between Spurs and Chelsea, dating back to at least 2005 and Frank Arnesen's acrimonious exit to west London, so any deal between the two clubs would be extremely difficult to pull off. Not to mention the on-field rivalry.
City are looking for a new talisman with Sergio Aguero leaving in the summer, though Pep Guardiola last month ruled out an expensive replacement if any at all.
He said: "Listen, with these prices (£100m-plus) we are not going to sign any striker – we cannot afford it, it’s impossible. That’s not going to happen, no. All the clubs struggle financially and we are not an exception.
How much would Kane cost?
It is understood that only figures in the region of £150m and further north would be enough to have Daniel Levy even consider a sale.
The official line from Spurs is that Kane is not for sale at any price, and it’s true that the club holds all the cards. Levy can vow to honour Kane’s agreement, but he is under no pressure to do if the player’s market value - or Levy’s own valuation - isn’t met.
Kane has three years remaining on his contract so Spurs are under no pressure to sell, more so with the financial constraints that a post-Covid market would pose potential suitors.
Levy, who drives the hardest of bargains - especially when it comes to selling key players - just ask Gareth Bale or Luka Modric.
What has Kane said?
Regarding wanting to leave, absolutely nothing.
He has, as mentioned above, previously underlined statements of his happiness at Spurs with a warning that he is prepared to leave should he start to believe his ambitions are not, or will not, be met. He wants to win everything in the game and is an extremely driven player.
In 2016, Kane said: As long as there's a vision with the club, and we're not stale, we're going forward as a club ... I'd love to stay here for the rest of my career. We'll just have to see what happens."
Speaking in 2017, Kane told Thierry Henry in a TV interview: “In three years’ time, if I haven’t won a few trophies by then, I think it will be disappointing.”
Three years later, last season, Kane said: "The main thing [for next season] is a trophy. It's been about four years now that I've been playing at this level and we're yet to win a trophy.
"I wake up every morning and that's what I want to achieve. For me personally, though, I just want to improve. Every year I want to get better, to score more goals and to get more assists."
Around the same time last year, Kane told Jamie Redknapp: "I love Spurs, I'll always love Spurs but I've always said if I don't feel we're progressing as a team or going in the right direction, I'm not someone to stay there for the sake of it.
"I'm an ambitious player, I want to improve, get better and become one of the top, top players. It all depends on what happens as a team and how we progress as a team. So it's not a definite I'm going to stay there forever but it's not a no either."
What have Tottenham said
When contacted by Standard Sport for comment on the latest reports, Spurs released the following statement.
It read: "We have a season to finish and we want to finish it as strongly as possible. That's all everyone should be focussing on."
On Tuesday, interim manager - and very close friend of Kane - Ryan Mason insisted Kane was “100 per cent committed” and had not spoken to the club to request a transfer.
“I don’t think anything is awkward,” he said. “There’s always speculation around the best players. There’s been speculation in the last three or four weeks about the new manager coming in, all these question marks.
“Which is normal when you’re at a big club, that’s normal. Our focus – and I’ve said it all along – is on the next game.
Next club odds
Man City: 2/1
Man United: 13/5
Real Madrid: 20/1
Odds via Betfair (subject to change). Click here to find out more.