Jurgen Klopp's side have beaten Bayern to the Bundesliga title for the last two seasons, with Dortmund also winning the German Cup last season.
Schweinsteiger thinks that Bayern's promising early season form can be put down to their determination to challenge Dortmund this time around.
The German international said: "I believe that Dortmund have played a key role in our results so far. If they had not been around, we would probably no have made the progress we have made now.
"Winning the Bundesliga is our top priority at the moment. However, I think that we can aim even higher this season."
Bayern sit top of the table at this early stage of the season, with a 100% record after five matches.