Kane is considered 'untouchable' - with the Premier League side hoping to tie him down to a new contract amid transfer speculation.
But it appears Bayern will test Spurs' resolve over Kane, according to Italian journalist Alfredo Pedulla.
The German giants have enquired to see whether it would be possible to sign the England international this summer.
Spurs, however, are reluctant to sell their prized asset and have offered him a new contract with his current deal set to expire in 2024.
Other than his loan spells, Kane has stayed loyal to Spurs who are hoping he remains at the club for the rest of his career.
Kane enjoyed another prolific campaign this season, scoring an impressive 27 goals in all competitions.
He starred in the second half of the season as he inspired his side to a top four finish, securing Champions League football.
The reported interest in Kane comes after Bayern were unsuccessful in their opening bid for Sadio Mane.
They're thought to be keeping tabs on the Liverpool star in view to replacing Robert Lewandowski, who wants to leave the club this summer.
After eight ultra-prolific and trophy-laden seasons at Bayern, the 33-year-old is seeking a move away from Germany.
Barcelona are believed to be in the running to sign the Poland international.
He's scored an incredible 344 goals for the club since his move from Borussia Dortmund in 2014.
Will Bayern draft in Mane or Kane if Lewandowski leaves? Watch this space.