The new Premier League champions are in the market for a striker this summer as a result of Diego Costa heading towards the door. It had been expected to be a reunion with Romelu Lukaku, but the Blues may have eyed an opportunity to land a genuine superstar.
According to the Daily Mirror, Chelsea have made a 'serious enquiry' in an attempt to seemingly gauge the likelihood of a deal being possible.
It comes after 28-year-old Lewandowski was apparently left distraught on the final day of the Bundesliga season when he was gazumped by Borussia Dortmund's Pierre-Emerick Aubameyang and missed out on being the division's top goal scorer for the third time.
Lewandowski had netted 30 times in the league but fired a blank that day, and it appears that he holds other responsible. He has already accused team-mates of not supporting him enough, with coach Carlo Ancelotti also now coming into his firing line as well.
"Robert told me that he got no support and that the coach gave no call to help him in the last game to win the top-scorer title," agent Maik Barthel is quoted as saying.
"He was disappointed as I have ever seen him before."
Bayern landed Lewandowski as a free agent from Dortmund in 2014 and given the fees that have been paid in recent seasons and that are being talked about now for others, the German champions could easily command an enormous price if they were at all willing to sell.
One would have to expect that if Chelsea are to have any chance of striking a deal, the £75m that Juventus paid for Gonzalo Higuain last summer would be the minimum amount.