Kompany confident Kane will be fit to face Aston Villa
Kane, who has a history of ankle problems, was replaced in the closing minutes of Saturday's home 1-1 draw with reigning Bundesliga champions Bayer Leverkusen.
However, the England captain was able to return to training on Tuesday.
"Harry trained today, and things went well. But we need to wait and see till tomorrow and be sure things stay like that," said Kompany at his pre-match press conference.
"Then we can calmly make the right decision. Hopefully everything stays fine."
Bayern are unbeaten in Kompany's opening seven games in charge with the Leverkusen stalemate the only match the former Manchester City captain failed to win.
The German giants have been in scintillating form, including a 9-2 thrashing of Dinamo Zagreb on matchday one of the Champions League.
Kompany was a surprise choice to land one of European football's top jobs after overseeing Burnley's relegation from the Premier League last season.
The former Belgian international said he had nothing to prove on his return to England.
"I don't have to prove anything as a coach. I think it's important to keep things separate," he added.
"Every challenge you take on has a different context. The most important thing for a coach is to say: 'Have I really done everything I can to get the best out of the team?'
"When you come home every night, you might say I'm tired, but if I've done everything I can to make the team better, I'm happy.
"I have a new club, a new team, a new task. You have to leave the past behind you. It's not about me now, it's about the players and the club."
Villa also got off to a winning start in their first taste of Champions League football for 41 years in a 3-0 win at Young Boys.
But it is the visit of Bayern in a repeat of the 1982 European Cup final won by Villa that has been eagerly awaited by fans of the Premier League side.
"What they did last season was extraordinary. They've earned it," said Kompany, after Villa beat out the likes of Chelsea, Manchester United and Tottenham to finish fourth in the Premier League.
"They're a really organised team with a good atmosphere at home. But Bayern are used to these nights. We want to enjoy it, and the players are hopefully up for playing here."
