Bayern made it 13 wins from 13 matches across all competitions when they eased past hosts Borussia Monchengladbach 3-0 on Saturday to top the Bundesliga with a maximum 24 points from eight games.
Their 13-match run equalled the record for the best start to a campaign in Europe's big five leagues, which had only been achieved by AC Milan in the 1992/93 campaign.
"We are doing a lot of things right at the moment and we have to take this into the next game," Kompany told a press conference. "Until now Koln have done it well. You have to give them credit for what they do in defence. They operate with a lot of urgency.
"They play at home so they have every right to believe in their chances. But we are very hungry for this Cup."
Bayern, who last reached a German Cup final in 2020, have a busy week with three matches in seven days, starting with the trip to Koln on Wednesday.
They host in-form Bayer Leverkusen in the league on Saturday before Tuesday's Champions League match against holders Paris Saint-Germain.
"The hunger for tomorrow is big," said Bayern sports director Christoph Freund. "It is a knockout match. Everyone has the great wish to go back to Berlin (for a German Cup final)."