The Bayern coach was speaking in Hong Kong before Friday's pre-season friendly against Aston Villa, with the Bundesliga champions preparing for another campaign in which they will be expected to challenge for every major trophy.
Bayern completed a domestic league and cup double last season but fell just short in Europe, losing a dramatic Champions League semi-final 6-5 on aggregate to eventual winners Paris Saint-Germain.
Kompany admitted matching last season's achievements would not be easy but said Bayern had to set the highest possible standards.
"Right now, I will say our goal is to win the Champions League," Kompany said.
"During the season, I will tell you we have to focus on the next game, because you cannot win the Champions League in September, you cannot win it in October."
He believes Bayern's transfer recruitment has improved the squad and could give them a better chance of ending their wait for European success.
"I think we have improved a little bit as well on the squad, with some of the transfers," he said.
"Hopefully this gives us a chance to achieve our goal. It's tough to do better than last year, really tough, but it has to be our goal."
The German champions have added Morocco midfielder Ismael Saibari from PSV Eindhoven and Germany defender Nathaniel Brown from Eintracht Frankfurt as they continue to strengthen the squad.
Several players involved in the 2026 FIFA World Cup, including Harry Kane and France forward Michael Olise, were not part of Bayern's tour of Asia.
Kompany also dismissed speculation linking Olise with a move to Real Madrid, insisting the forward's future had never been in doubt.
"The topic was never open for me," Kompany said.
When asked about reports concerning Olise's private life, Kompany declined to comment.
"Private life is private life," he said.
Thousands of supporters attended Bayern's open training session at Hong Kong's Kai Tak Stadium ahead of the meeting with Aston Villa.
Villa continue their own preparations after a busy transfer window. The Premier League club are adapting to life without Morgan Rogers following his move to Chelsea for a reported British record fee of 117 million pounds.
The Europa League winners have responded by signing Swiss midfielder Johan Manzambi for a club-record fee, bringing in Joao Gomes from Wolves and securing Alejandro Garnacho on loan from Chelsea.
Friday's match is Villa's final game of their Asian tour before they face Paris Saint-Germain in the UEFA Super Cup next week.
Bayern begin their Bundesliga title defence at home against Stuttgart on August 28, while Villa open their Premier League campaign away to Brighton on August 23.
