Kane is out of contract next summer and while Spurs are adamant their star striker is not for sale, rumours are rife that he'll depart the club within the next 12 months.
Bayern's pull is a strong one, as he'll be guaranteed goals and silverware, but Tottenham are remaining steadfast in their decision to retain Kane's services.
But for the most part, Bayern's official offer, while falling short, means Spurs should feel confident about quietly completing a bumper deal for James Maddison.
Leicester's relegation meant Maddison, among a number of others, was up for grabs this summer, and the England international wasn't short of potential suitors.
Newcastle were linked, while Arsenal, Manchester United and Liverpool had also been linked with a move for the 26-year-old.
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However, even without the lure of European football, Spurs look to have won the race for Maddison's services.
Following on from the permanent capture of Dejan Kulusevski earlier this month, it's been a solid start to the window for Spurs.
The appointment of Ange Postecoglou looks to have settled the club down following a turbulent end to a campaign that promised so much, but ultimately fell well short of expectations.
With the Australian's arrival comes a change in system at the club, and Postecoglou is expected to move away from the three-man backline Antonio Conte favoured to a 4-3-3 setup.
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However, the issue is that the players at Postecoglou's disposal don't fit the system, notably in midfield. A problem last season was that Spurs lacked a player to knit together the midfield and attack, particularly in the wake of Rodrigo Bentancur's season-ending knee injury at Leicester back in February.
In Conte's preferred 3-4-3 system, the wing-backs were the ones tasked with creating the chances, yet they lacked the creative presence in the final third to pry apart defences. `
As Conte's infamous reign in north London entered its final weeks and the wing-backs failed to have the desired effect, Spurs' season ground to a halt that meant they not only missed out on a top-four spot, but failed to even make the Europa League and Conference League.
The hope then is that Maddison can provide the missing link. He ended 2022/23 with 10 goals and nine assists to his name, an impressive haul in a Foxes outfit that succumbed to relegation on the final day of the season.
A WhoScored.com rating of 7.24 was the second best of those to not finish inside the top seven, and it ranked 15th overall. Maddison was head and shoulders above the rest at the King Power Stadium.
Maddison's exit was inevitable and Spurs are certainly going to benefit immeasurably from his arrival at the Tottenham Hotspur Stadium.
Postecoglou's ideal midfield is to operate with two midfield 'eights' and one midfield 'six' to shield the defence and keep play ticking over. The former pair have the freedom to get forward and support the attack, so much so that one can, at times, act as a second striker.
Celtic last season, on occasion, looked as though they were operating in a 4-4-2 when out of possession as Matt O'Riley pushed on to line up alongside Kyogo Furuhashi to help pressure defences and force mistakes.
In theory, Maddison could operate in a similar way to help Spurs press high up the pitch. He may have won possession in the attacking third just 18 times in the Premier League last season, that ranking 58th, but an average of 1.8 tackles per 90 shows that Maddison is prepared to carry out the nitty gritty hard work off the ball as another avenue in creating chances. In possession, though, is where supporters will see the attacking star at his best.
Maddison ranked tenth for key passes (69) in the Premier League last season, while compared to Spurs' current crop, Son Heung-Min (61) came closest to matching the former Norwich man.
In addition, 12 big chances created was the 11th best in England's top tier. What will also appeal to Postecoglou about Maddison, though, is his versatility. As mentioned, the 57-year-old favours a 4-3-3 system, but that doesn't mean the impending new arrival will only play in the middle of the park.
On occasion last season, Maddison played on the right, and while this is a role that Kulusevski is set to play, the interchangeability of the pair means that Postecoglou can move the duo around on the right flank as and when needed. Theoretically the Swede can operate in one of the two 'number eight' roles.
Discussing his best position last year, Kulusevski said: "I always thought of me being a number ten, I still think I am, but my best results as a football player have always come being a right winger, so I don't know!"
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However, Maddison will likely join Spurs to play in a central midfield role, and fill a void that has needed filling since the departure of Christian Eriksen for Inter Milan in January 2020.
The impending arrival of Maddison offers a slither of hope of a successful long overdue rebuild in north London as Spurs invest accordingly in a long-term target to help the Postecoglou era get off to the best possible start.