Bayern have dominated German football in recent years, winning the Bundesliga 13 times in the last 14 seasons. However, domestic success alone is not enough for a club with Bayern's ambitions, and European glory remains the ultimate prize.
Laimer echoed Kompany's desire to compete for every available trophy and said the players are fully committed to achieving that goal.
"When you're at FC Bayern, you always want to win every single title," Laimer said.
"The Champions League is part of that, the domestic trophies are part of that. That's what we train for every day. Personally, I'll do everything in my power to achieve that."
Bayern's European campaign begins on Thursday when they face Norwegian side Bodo/Glimt at the Allianz Arena.
Kompany's team have already made a strong start to the season, lifting the German Super Cup after beating Borussia Dortmund before producing an impressive 5-1 Bundesliga victory over VfB Stuttgart.
The Champions League will provide a much tougher test, though Bayern will be determined to go further than last season. They reached the semi-finals before being beaten by eventual champions Paris Saint-Germain.
