The 28-year-old was strongly linked with an exit from North London last summer and ended another season without winning a piece of silverware in 2021-22.
The arrival of Antonio Conte saw Tottenham pip Arsenal to fourth place in the Premier League, though, and Kane is now said to be open to staying at the club.
The England captain only has two years left to run on his current contract, but Spurs are thought to be planning talks over an extension for the striker.
Manchester City will not be moving for Kane after signing Erling Braut Haaland and Julian Alvarez, while Manchester United could be spending a big chunk of their budget on Frenkie de Jong.
Former Bayern goalkeeper Kahn has ruled out the prospect of his side making a move for Kane this summer, in spite of the fact that Robert Lewandowski is now confirmed to be joining Barcelona.
However, the 53-year-old has insisted that a move for the Tottenham man is still a "dream", telling German outlet Bild: "He is under contract at Tottenham. Sure, he is an absolute top striker, but that's all a dream of the future. So let's see what happens."
Kahn has also ruled out the prospect of his side making a move for Cristiano Ronaldo, who is believed to have told Manchester United that he wants to leave in the current window.
"I love Cristiano Ronaldo and everyone knows what a fantastic player he is. But every club has a certain philosophy and I'm not sure if it would be the right signal for Bayern if we signed him," Kahn added.
At the other end of the field, Bayern are seemingly set to win the race to sign Juventus centre-back Matthijs de Ligt, who has also been persistently linked with a Premier League switch.
Chelsea were thought to have been in talks to sign the 22-year-old, but the Blues have instead signed Kalidou Koulibaly and are now focusing their efforts on Presnel Kimpembe or Jules Kounde.
As a result, Bayern have stolen a march in the race for De Ligt, and Kahn has now claimed that the former Ajax defender is pining for a move to the Allianz Arena.
"We had talks and the player wants to come to FC Bayern. We'll have more discussions and then see how it goes," Kahn said in a separate interview with Blickpunkt Sport.
As is the case with Kane, De Ligt is also due to become a free agent in 2024 and could supposedly be allowed to leave Juventus for a £76m figure in the coming weeks.
Bayern have already lost one central defender this summer in the form of Niklas Sule, who joined Borussia Dortmund on a free transfer after five years at the Allianz Arena.
Lewandowski, Omar Richards, Marc Roca and Corentin Tolisso have also left the club, but a new deal has been agreed with in-demand attacker Serge Gnabry until 2026.