Kane had been sidelined with an ankle injury, missing England's recent friendly defeat to Japan and Bayern's 3-2 Bundesliga win at Freiburg. However, his return to training has given the German champions hope ahead of one of their biggest matches of the season.
"It was important that he did a lot of training today," Kompany said. "I don't think he's lost his rhythm. We'll wait until tomorrow and then decide."
Kane's potential return would be a major lift for Bayern. The England captain has been in outstanding form, scoring 48 goals in 40 appearances across all competitions this season, underlining his importance to the team's attacking threat.
Kompany confirmed that, aside from goalkeeper Sven Ulreich, he has a full squad available. "We have a strong squad and we're ready for the two legs," he added.
Bayern travel to Madrid in strong form, sitting comfortably at the top of the Bundesliga and showing consistency in Europe, where they lost just once en route to the knockout stage.
In contrast, Real Madrid come into the match looking to respond after a recent La Liga defeat to Mallorca, despite their dominant 5-1 aggregate victory over Manchester City in the previous round.
Kompany insisted his players must approach the game with belief and focus. "The most important thing is that we have full focus on the game tomorrow. We want to show what we're capable of," he said. "I just want us to win and not have any fear."
The Bayern boss acknowledged the challenge of facing the Spanish giants away from home but backed his side's experience.
"Everything will matter tomorrow," Kompany said. "This is my first time here as a coach, but we have a lot of experience in games like this. It's perhaps the toughest away game you can play, but we want to win."
