The Poland striker did not mention Bayern by name but told Sport Bild magazine he was keen for a move to his "dream club" to happen this month rather than playing out the final year of his contract with Dortmund.
Lewandowski, 24, has reportedly already agreed terms with Bayern, and will join next summer if not this.
"I expect everything to be cleared up now so that I will be allowed to move to my dream club this summer," he said.
"That would be the best for everybody involved."
Should Lewandowski move to the European and Bundesliga champions, he would follow team-mate Mario Gotze, whose controversial transfer was confirmed just prior to Dortmund's Champions League semi-final tie with Real Madrid.
His loss would therefore be a second major blow to the 2011 and 2012 Bundesliga champions as they bid to keep up with record-breaking Bayern next season.
Lewandowski says his preference to leave is not because he is unhappy in Dortmund.
"Dortmund are a fantastic club whom I will always admire," he said.
"It's just now I want a new challenge for my future."