Will he move to Bayern Munich? Can Manchester United convince Tottenham to sell? Is he going to sign a new deal?
It's a transfer adventure that shows no signs of letting up. Unlike Hugo Lloris, who was left in London to negotiate a transfer away, Kane has made the pre-season trip to Australia.
But, even so, Spurs need to consider their options in the event he does leave for pastures new this summer.
Here, WhoScored.com have picked out five potential Kane replacements Spurs could target should the England captain depart before next month's deadline.
Ivan Toney - Brentford
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Ivan Toney is unable to play again until January following his ban by the FA, and Brentford should feel confident they can retain the services of last season's top scorer.
However, reports today suggest Tottenham are looking to the England international as a potential replacement for compatriot Kane.
Toney was superb up until his suspension for the Bees last term. Only Erling Haaland (36) and Kane (30) scored more goals than the 27-year-old (20) in the 2022/23 Premier League season and Brentford will certainly miss their star forward for the first half of the coming campaign.
Given his striking approach and style of play, Toney could well be considered the perfect fit for Ange Postcoglou's Spurs. While he won't drop deep in the same vein as Kane, the Brentford hitman is more than capable of operating as the lone frontman and giving defences a torrid time.
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Dusan Vlahovic - Juventus
Dusan Vlahovic hasn't quite lived up to expectations following his move to Juventus from Fiorentina 18 months ago, netting just 17 league goals in that time, but in this dysfunctional Old Lady outfit, that isn't to be scoffed at. Like Toney, the Serb is a different profile to Kane, in that he prefers to get on the end of chances rather than drop deeper in search of possession.
In truth, this may be the type of striker Spurs do need this summer. Kane's tendancy to drop deep worked well when they didn't have a creator in midfield, but the arrival of James Maddison may complicate matters in a key area of the pitch. Vlahovic is more the traditional number nine, and this could work to Spurs advantage.
Juventus won't sell for cheap, while PSG are also sniffing around the 23-year-old, but the Serbia international could prove a suitable replacement for Kane.
Goncalo Ramos - Benfica
While Spurs have been linked with a move for both Toney and Vlahovic, Goncalo Ramos is one who has eluded gossip columns in the north London side's potential quest for a Kane replacement. Only Mehdi Taremi (21) scored more goals than Ramos (19) in Liga Bwin last season, and the 22-year-old's stock has soared following Darwin Nunez's move to Liverpool last summer.
Ramos really shot to prominence at the World Cup, where he netted a hat-trick in Portugal's 6-1 mauling of Switzerland in Qatar. The youngster is again more of a finisher than a link up man, but if his teammates create the opportunities, chances are Ramos will score.
Only Taremi (18) ranked better for big chances scored (16) in Portugal's top tier last term and while links with a high profile switch to Manchester United or PSG continue to do the rounds, Spurs would offer the promise of regular game time in a system that would play to his strengths.
Jonathan David - Lille
Moving over to France now, Jonathan David ended the 2022/23 Ligue 1 campaign with 24 league goals to his name; only Kylian Mbappe (29) and Alexandre Lacazette (27) bagged more than the Canada international. There has been little chat of David departing Lille this summer, but rumours of late have linked Tottenham with a move for the 23-year-old.
Only Lacazette (22) scored more clear-cut chances than David (19) in France's top tier last term, so like Ramos, if the opportunities are created, then he'll routinely hit the back of the net.
While David may not be the most physically imposing in the manner of the above trio, the Canadian still routinely hit the back of the net as the lone frontman in Lille's favoured 4-2-3-1 system. This experience in the role certainly weighs in his favour.
Evan Ferguson - Brighton
Another linked with a move to Spurs, Brighton may be reluctant to lose the prodigious Evan Ferguson this summer, but they do have frontmen in reserve were they to cash in on the teenager in Danny Welbeck, Deniz Undav and summer arrival Joao Pedro.
Ferguson ended the season with six league goals to his name in a solid breakout year under Roberto De Zerbi.
The teenage forward has drawn comparisons with Kane, and with a willingness to drop into space, it is easy to see why. Like David, he isn't the same stature as the likes of Toney and Vlahovic, but he is prepared to drop in to receive the ball and create for others, which could benefit the widemen in Postecoglou's 4-3-3 setup.
Pedro - Flamengo
Pedro has only recently been linked with a move to Tottenham as the club identify potential Kane replacements. The Brazil international hasn't exactly lit up the 2023 Brasileirao campaign, scoring just four goals across 12 league outings, while he endured a failed stint in Europe four years ago, struggling with Fiorentina before returning to his homeland.
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Yet he did enough to make Brazil's 2022 World Cup squad, playing as backup to current Spurs man Richarlison. Pedro is a different striker to Kane in that he prefers to operate primarily in the penalty box where he can maximise his goalscoring prowess.
The 26-year-old isn't the quickest, however, which may impact a Spurs side that'll look to break forward at speed under Ange Postecoglou, yet he's strong in the air and able to finish with both feet, so if the chances are created, he'll be confident of hitting the back of the net.