The 23-year-old was in lethal form for Dortmund last season scoring 30 times as they won their second consecutive Bundesliga title along with the German cup.
His goalscoring exploits have captured the attention of many managers around Europe with Blues boss Roberto Di Matteo one of them as he searches for striking reinforcements.
Di Matteo has brought Eden Hazard, Marko Marin and Oscar in to offset the loss of Didier Drogba and Salomon Kalou but still wants to add a new forward to his squad.
Fernando Torres is likely to start the season at the tip of the Italian’s three-pronged attack but only possesses one senior backup in the form of Daniel Sturridge, who played most of his football last term on the right of midfield.
The former West Brom chief has doubts as to whether can provide serious competition for Torres and operate alone up front should he be pressed into action.
Signing Lewandowski may prove to be problematic for the West London club after their initial £17 million bid was rejected by Dortmund as they are holding out for £20m.
Owner Roman Abramovich is looking to dial back on the heavy spending after splashing out over £60m on new players but knows Di Matteo requires a new frontman.
Should they be priced out of a move for the Poland international it’s thought Chelsea will focus their attentions on Willian after he professed his desire to Shaktar Donetsk for England.
An enquiry has already been made for the Brazilian who was said unhappy with the Russian giants after they rejected Abramovich’s offer.
Benfica’s Oscar Cardozo is also an option in the event that he fails to strike a deal for either Willian or Lewandowski although the 29-year-old Paraguay striker is considered a last resort.