Kane signed a four-year deal with Bayern last month after Spurs reluctantly agreed a package worth at least £100million with the German champions, rather than risk their record goal-scorer running down his contract and leaving for nothing in a year's time.
The England captain spent two decades at Spurs after joining the club as a schoolboy and in a video message to supporters after joining Bayern, he raised the possibility of a future reunion, saying: “It’s not a goodbye, because you never know how things pan out in the future... I’ll see you soon.”
Speaking at a fan forum on Tuesday, alongside manager Ange Postecoglou, new men’s captain Heung-min Son, women's head coach Robert Vilahamn and captain Bethany England, Levy suggested Spurs have the option to bring Kane back to the club in future.
Asked by one of the 250 supporters in attendance if Spurs had a buy-back clause for Kane, Levy initially did not answer but pushed by host Nihal Arthanayake, the chairman replied: "Of course."
Speaking ahead of Bayern's Champions League opener at home to Manchester United on Wednesday, Kane revealed he would always look out for Spurs' progress.
“I’m always keeping an eye on them and I’ll keep an eye on Tottenham for the rest of my life,” Kane said.
“I’m really happy to see the team playing the way they are and to see the fans happy is a great thing. They’ve got a massive game coming up [Arsenal on Sunday] so, for sure, I’ll see how they get on over the course of the season.”