Spanish publication 'AS' reports that the Poland international has his heart set on the switch and is now set to do whatever it takes to make a deal happen.
Bayern are understandably unwiling to lose their star man, with Lewandowski having scored 100 goals in just 121 appearances for the Bavarian side.
The aformentioned source goes as far as to saw that Bayern have already begun to line up replacements for the powerful Pole, with Chelsea's Alvaro Morata, PSG's Edinson Cavani and RB Leipzig's Timo Werner all thought to fit the bill.
Bayern's interest in Cavani raises an interesting prospect, with PSG also thought to be admirers of Lewandowski, though the 29-year-old appears to be set on a move to the Bernabeu.
Reports over recent weeks have claimed that 'Los Blancos' have already agreed a deal for Lewandowski, with Zinedine Zidane having been told that the striker will be a Real Madrid man come the summer.