Reports had claimed that the Bavarians' interest in the Polish international had cooled after it was announced earlier today that they had agreed to sign his Dortmund teammate Mario Gotze for £32m at the end of the current season.
Recent speculation has also suggested that Lewandowski was keen to listen to any offer that English champions Manchester United had to make him.
However, with Mario Gomez believed to be nearing a move to Juventus, Bayern are eager to land Dortmund's leading goalscorer as a replacement for the German international, according to Goal.com.
With Gomez potentially gone, Bayern would be able to offer 24-year-old Lewandowski regular starting action alongside Mario Mandzukic. Whereas, as it stands, United have Robin van Persie, Wayne Rooney, Javier Hernandez and Danny Welbeck in the striking positions.