The London native is one of the most prolific forwards this season as Kane scored 22 goals in 17 matches including the UEFA Champions League appearances.
Nkunku and Fullkrug scored 16 goals each in the 2022-23 Bundesliga campaign to share the last season's top scorer trophy in May.
This season in Bundesliga, Kane has averaged 1.5 goals per game.
Kane surpasses Bayern legend Gerd Muller
Kane has scored 17 goals in 11 Bundesliga matches to be the first player to do so in the league history.
Gerd Muller, Bayern Munich's legendary forward who died in 2021, had 17 league goals in the first 12 games of the 1968-69 season.
Kane's goal against Cologne on Nov. 24 was his 18th goal after 12 league matches, which is a new Bundesliga record.
Bayern won that match 1-0.
Top-scoring English player in Bundesliga
Bundesliga confirmed that Kane became the "most prolific English goal scorer" in a single season in the German top-flight league after scoring his 18th goal against Cologne.
Kane beat former Borussia Dortmund winger Jadon Sancho, and ex-Hamburg player Kevin Keegan, who scored 17 goals each in previous seasons.
In the 2019-20 Bundesliga season, Sancho, who currently plays for Manchester United, scored 17 goals for Borussia Dortmund.
Former England forward Keegan set record of 17 goals 1978-79 season while playing for Hamburg before his compatriot Sancho tied in 2020.
Separately Kane led Bayern Munich to a dominant "Der Klassiker", or German Clasico, win in a German Bundesliga week 10 match on Nov. 4, scoring a hat-trick against Borussia Dortmund.
He became the first player to score three goals in his first 'Der Klassiker'.
Bayern won 4-0 at Dortmund's Signal Iduna Park.
England star eyes Lewandowski's record
Kane, who bagged 18 league goals in 12 matches, now eyes ex-Bayern Munich forward Robert Lewandowski's goal scoring record.
Polish forward Lewandowski, who left Bayern Munich for Barcelona in 2022, scored 41 goals in a single Bundesliga season (2020-21) to be the record holder in this field.
Lewandowski has done it in 29 matches.
The 35-year-old broke Muller's 40-goal record that he set in the 1971-72 season.
Kane targets his first trophy at Bayern Munich
England captain Kane was a Tottenham regular in 2013-2023 did not win any trophy at the London club.
So he targets his first title at the German powerhouse.
Kane scored 278 goals in 430 matches for Tottenham. He was the Premier League's top scorer for three seasons (2015-16, 2016-17, and 2020-21).
The experienced forward made his Bayern Munich debut in a German Super Cup against RB Leipzig in August. But Leipzig won the local trophy over a 3-0 victory against Bayern Munich.