The highly-rated full-back thinks that his side will come out on top in their last group game, and is also committing his short-term future to Bayern Munich
Die Mannschaft head into their final Group B game in a relatively comfortable situation as they only depend on themselves to progress after defeating Portugal and Netherlands in their first two matches.
Lahm warned his team-mates against underestimating the Danes, but made it clear that he expects Germany to emerge from the contest as winners.
"They defeated Netherlands, and against Portugal they had a draw in their pocket right until the end," he told Bild.
"Denmark are a difficult opponent, they are very well organised in defence. And in attack they have Nicklas Bendtner, who is a very dangerous striker with a lot of international experience.
"But I am convinced that we will win and become the first team to progress from the group stage with nine points."
Germany's quest for the World Cup 2010 title was cut short in the semi-finals following a 1-0 defeat to Spain, and Lahm believes that his side have improved a lot since then.
"In comparison to the World Cup squad, we have become more mature, and we are now one of the co-favourites to win the European title," the 28-year-old added.
"We have shown [why] with our victories against Portugal and Netherlands. But the matches were very close.
"That is right. We all think that we have even more potential."
Meanwhile, Lahm's future at Bayern Munich has been a hot topic of debate in recent days, with the full-back refusing to commit his future to the Bavarian giants earlier in the week amidst speculation that Real Madrid are interested in his services.
"In football, you should never say never," he conceded. "That is why I cannot promise that I will play at Bayern until I am 32 [his contract expires in 2016].
"But to calm everyone down: I am firmly convinced that I will play at Bayern next season. I am very comfortable in Munich."