Kane, who is Tottenham’s all-time record goalscorer, departed his boyhood club in August to join the German champions.
Tottenham held out for a fee that could rise to £120m for the England captain, with Kane set to enter the final year of his contract with the Premier League club.
The 30-year-old signed a four-year deal with Bayern and has set his sights on winning the Champions League with the German side, ahead of the start of their European campaign against Manchester United on Wednesday night.
But Kane, who scored 280 goals for Tottenham, has deep emotional ties with Spurs and chairman Levy revealed there was an option inserted into their deal with Bayern to potentially re-sign the striker in the future, although he did not reveal what the fee would need to be.
Levy made the comment at a Tottenham fan forum and confirmed “there is a buy-back clause” when asked about Kane’s departure.
In his departure video upon leaving Tottenham last month, Kane left open the possibility of a return to Spurs in the future.
“I’ll be watching this season, good luck to Tottenham, good luck to the whole club so it’s not a goodbye because you never know how things pan out in the future but it’s a thank you and I’ll see you soon,” he said.
Kane has scored four goals in five appearances since joining Bayern, while Tottenham have made an impressive start in the Premier League under new manager Ange Postecoglou.
Spurs have won four of their opening five games, drawing the other, and face rivals Arsenal on Sunday as they look to extend their best start to a league season since 1965/66.