"We still have to wait a bit but I say I think in January I can go," the 25-year-old told reporters after Tuesday's 2-0 German Cup second-round win against 1860 Munich.
Asked whether that would mean a move to Bayern in January, Lewandowski, with a Dortmund official standing nearby, said: "Yes, because it is then that I can officially sign a new contract."
The Poland international fell out with Dortmund bosses over his failed attempt to join the treble winners in the close season but recently said ties had been mended and accepted the fact that he would spend more season there.
Dortmund opted not to sell Lewandowski, who joined in 2010 and won consecutive league titles in 2011 and 2012 as well as the German Cup in 2012.
The Ruhr valley club were last season's Champions League runners-up, losing to Bayern, who have already snapped up Dortmund talent Mario Goetze this season, in the final.
Lewandowski's contract with Dortmund runs until June next year but January will be the last transfer window for the club to cash in on him. If he left after June, it would be as a free agent with the club missing out on a transfer fee.