The Poland international moved to the Allianz Arena in 2014 and has enjoyed incredible success with the Bavarians, scoring 117 goals in 153 games in all competitions, while he has already notched seven in six this term.
The 29-year-old has won the Bundesliga title in each of his three three seasons at the club, with every chance of making it four this time around.
However, he rocked the boat over the summer by questioning why the German champions had not matched the spending of Paris Saint-Germain and Barcelona.
Bayern CEO Karl-Heinz Rummenigge then revealed in an interview that he felt Real Madrid was "the club of Lewandowski's dreams".
According to Spanish outlet AS, there will be regular meetings between the player's representatives and Real this season with a view to a transfer next summer.