If they beat sixth-placed Mainz and second-placed Bayer Leverkusen fail to beat Augsburg at home, Bayern and Kane will be crowned Bundesliga winners.
Bayern are eight points clear with four games remaining, so a first title for Kane is a mere formality.
But after losing six finals - three with Tottenham, two with England and one with Bayern - a debut title win would be a long-awaited reward for the 31-year-old forward.
After two decades at boyhood club Tottenham, Kane moved to Bayern in 2023, motivated by a desire for team honours.
While Bayern's dreams of winning the Champions League in their own stadium this season flamed out with a quarter-final loss to Inter Milan, lifting the Bundesliga shield would soothe frustrations after a trophyless 2023/24.
Kane has rarely spoken about the title, preferring to focus on the task at hand, but in February he revealed how much the pursuit of a team honour drove him.
"There are many people who, throughout my career, only talk about the fact I haven't won a title yet. It would be nice to silence a few of them," Kane said.
Kane would also join Kevin Keegan and Owen Hargreaves as Englishmen who won the Bundesliga.
Speaking with Sky Germany on Wednesday, Bayern powerbroker Uli Hoeness - a key player behind the 100 million euro (£86.4m) decision to bring Kane to Bavaria - said "nobody deserves the title more" than the England captain.
Calling Kane "a real Bayern player", Hoeness lavished praise on the striker, saying, "he fights, he works, he scores an incredible number of goals, but he also works hard for the team.
"You can feel that he absolutely wants to win this title."