The Armenia international insists Dortmund's aim for the season is securing Champions League football, not trying to steal the Bavarians' crown
Jurgen Klopp's side got the season off to a fine start by beating the Bavarians 2-0 in the DFL-Supercup on Wednesday, with the Armenia international on the scoresheet.
However, the former Shakhtar Donetsk man remains pessimistic about his side's chances of title glory in the coming campaign and insists their immediate goal is Champions League qualification.
"It's going to be very difficult to challenge Bayern - they're an incredible strong team," he told the Bundesliga's official website.
"We have to do everything we can to make sure we finish in those top three places and qualify for the Champions League.
"That's our goal for the season. Anything more is going to be very hard for us."
Mkhitaryan came in for criticism during his maiden season in Germany but the 25-year-old is eager to add more to his game.
"I'm going to try to do more this season. I'll do my best. I don't want to stay at this level - I want to build on it. I always try to give my all in every game and in every training session to make the fans happy."