The 24-year-old is understood to have been identified by Roman Abramovich as a player he wants to add to his squad, as part of the deal that will see Kevin de Bruyne leave west London in the summer.
Bayern Munich are also keen on recruiting Lewandowski, but Chelsea are looking to steal a march on their rivals by incorporating the Poland international into the De Bruyne sale.
The Belgian winger has enjoyed a productive season-long loan spell in Germany with Werder Bremen, catching the eye of Borussia Dortmund boss Jurgen Klopp.
Now, Klopp wants to bring the former Genk star to the Westfalenstadion, but it's unclear whether he'll be willing to part with his star striker.
Having agreed a five-year contract in principal with Borussia Dortmund, all that is holding up the deal is Chelsea's ongoing negotiations to try and lure Lewandowski.
Failure to reach agreement over the prospective player-plus-cash transfer will see Chelsea demand £14million from the Bundesliga club for De Bruyne's services.