Speaking after Bayern's 3-0 win over Atalanta on Wednesday, the England captain said the team had learned and evolved under Kompany's guidance. "We've really honed in on his ideas now," Kane said. "Last season was his first with us, and we were still learning. This year, we're a stronger team, and that shows on the pitch."
Bayern sit nine points clear of Borussia Dortmund at the top of the Bundesliga and face Union Berlin on Saturday at the Allianz Arena, with the German Cup semi-final against Leverkusen and Champions League quarter-final clash with Real Madrid looming in April. A treble would make Bayern the first European men's side to achieve the feat.
Kane, who has scored 30 league goals this season, is closing in on Robert Lewandowski's single-season Bundesliga record of 42 goals.
Bayern have netted 93 goals in 26 games, just eight shy of their all-time league record of 101. "Now it's about proving it on the big stage," Kane added. "April and May is when it really counts. We have to be at our highest level in those moments."
Michael Olise is also on course for a record-breaking season, with 17 assists, five shy of Thomas Mueller's Bundesliga record.
Bayern's run has been strong, with just two defeats in 41 games across all competitions, but Kompany's side will face challenges against Union Berlin. They will be without injured stars Jamal Musiala, Manuel Neuer and Alphonso Davies, alongside suspended players Nicolas Jackson, Jonathan Tah and Luis Diaz.
Kane acknowledged the absences but insisted the squad was ready for the pressure.
"We've had a fantastic campaign so far," Kane said. "Even with a few players out, we know we can step up and perform when it matters most."