Kane has entered the final year of his contract with the North London club and has been linked with a move away in the next few weeks.
The likes of Real Madrid, Chelsea and Manchester United have been credited with an interest in the England captain but it is the German champions who looks to have stolen a march on their rivals to secure Kane.
A £70m bid has reportedly been tabled by Thomas Tuchel’s side, who have also held discussions with Kane’s father and brother, who doubles as his agent.
Bayern Munich’s honorary president Uli Hoeness believes a positive outcome will eventually emanate from fruitful discussions held with the 29-year-old.
“Harry Kane has clearly signalled in all conversations that his decision stands – and if he keeps to his word then we’ll get him, because then Tottenham will have to buckle,” Hoeness told German TV channel Sport1.
“Kane wants to play internationally and luckily for us Tottenham will not be active internationally next year.
“He now has another opportunity to come to a top club in Europe.
“Up to now, the father and the brother have always stood by what they promised. If it stays that way, that’s OK.”
Kane scored 30 Premier League goals for Tottenham Hotspurs last season.
