However, he has his heart set on the biggest two.
The Germany international believes Bayern are good enough to win the Champions League and is confident Germany are primed for glory at Euro 2012.
And that's without mentioning the Bundesliga and DFB-Pokal, for which Bayern are odds-on favourites after an impressive start to the season.
"I have a goal for this season and that is to win the Champions League in Munich and then become European champions in Poland and the Ukraine," Schweinsteiger told the Bild newspaper.
"To win this double title with Bayern and the national team now seems more possible than in recent years."
Bayern have an extra incentive to lift the Champions League this season since the final will be staged at their Allianz Arena.
"Knowing the final is in our own stadium is not a burden for us," he said.
"In my opinion, we are stronger than in the last two years, and that is why I say that we are one of the five or six favourites to win the Champions League."
Bayern have already opened their challenge for Champions League glory with a play-off win over FC Zurich and they begin their group stage campaign at Villarreal on Wednesday.
Manchester City and Napoli are their other opponents, which is why Schweinsteiger is being cautious.
"We all have this goal on our minds, but we also all know that it is a long and difficult way to get there," he added.