That has forced the European champions to revive their interest in record-breaking Lewandowski as they try to give boss Thomas Tuchel the prolific goalscorer he wants.
But Chelsea face a fight on their hands to bring Bayern to the negotiating table for the Poland international.
The German champions want Lewandowski, 32, to sign an extension to his current deal, which does not expire until 2023.
He broke Gerd Muller’s longstanding record for Bundesliga goals in a season by notching his 41st in the last minute of the final game of last season.
But Lewandowski is keen for one last adventure before his illustrious career ends and would relish a move to the Premier League.
Bayern are not unsympathetic to his desires but know that selling their talismanic striker, especially without a suitable replacement, would send a bad message.
Manchester City had been linked with Lewandowski but Etihad sources last week ruled out a move.
But Chelsea have the financial resources to test the German club’s resolve.
Lewandowski turns 33 next month and even Bayern’s head could be turned by a big bid for a player whose price will plummet if he runs down his contract.
Chelsea head coach Tuchel now regards the Pole as his best option in a tricky transfer market.
Tuchel watched Hakim Ziyech score a hat-trick as Chelsea kicked off pre-season with a 6-1 thrashing of Peterborough at their Cobham training HQ.
The Blues, who finally sold Olivier Giroud to AC Milan yesterday, included forgotten man Danny Drinkwater in their side as well as the likes of Ross Barkley, Christian Pulisic, Tammy Abraham and Callum Hudson-Odoi.
