With trophies looking further away than ever, and Kane nearing his 28th birthday, he has decided he needs to leave the club and join one of Europe's biggest powers if he is to realise his dream of building a medal collection worthy of his considerable talent.
But the England captain is yet to win a major trophy and should he be allowed to leave Spurs, there will be plenty of big clubs willing to snap him up.
Jordan Cox, trader at Star Sports, said: "Manchester City seems to be the likeliest destination for Harry Kane this summer.
"We saw a rush of bets on City laying them all the way down from 3/1 into 7/4 joint-favourites with Spurs.
"Pep Guardiola's side are on the hunt for a new striker to replace Sergio Aguero and moving for Kane will be one of the most expensive transfers in English football history, but will Levy sell to a Premier League rival?
"We are 10/1 for Kane to be reunited with his former manager Mauricio Pochettino, whereas United have been drifters in the market out to 3/1 from 2/1 as they seem to have their sights set on a big-money move for Jadon Sancho this summer."
Manchester City (7/4)
As you can imagine, trophy magnets Manchester City are favourites to sign Kane at 7/4.
And with Kane on the hunt for regular trophies, this could be the best move for his career.
Pep Guardiola's side are in need of a new striker with record goalscorer Sergio Aguero leaving the club at the end of the season.
Will we see Kane playing at the Etihad Stadium next season?
Manchester United (13/5)
Local rivals Manchester United are at third in the betting at 13/5, but would Kane fit into their team?
The Red Devils have been linked with the forward for some time, although they may decide not to make a move with Edinson Cavani agreeing a new deal.
Kane could join his English counterpart in Harry Maguire, but would the defender hand over the armband?
Paris Saint-Germain (10/1)
A move to PSG would see Kane reunited with ex-Tottenham boss Mauricio Pochettino, which could tempt the player to head overseas.
Surely not, right?
The England striker may even remain in London yet, with Chelsea priced at 14/1 for his signature.
The Blues' first-choice striker Timo Werner has managed just six Premier League goals this term and they want a more prolific forward in Kane.
The move looks highly unlikely, though, especially given the bitter rivalry between the two London clubs.
Harry Kane next club odds (before September 3)
- Tottenham Hotspur 7/4
- Manchester City 7/4
- Manchester United 13/5
- Paris Saint-Germain 10/1
- Chelsea 14/1
- Real Madrid 20/1
- Juventus 25/1
- Barcelona 66/1
Odds are correct at the time of publication and are, as always, subject to change.
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