The Polish forward is out of contract in the summer having refused to sign an extension, and is believed to have already agreed terms with rivals Bayern Munich.
Lewandowski, who scored last night as Dortmund clinched their place in the last 16 of the Champions League with a dramatic 2-1 win over Marseille, said recently that he intended to announce his destination in January.
Although that is almost certainly Bayern, the Express claim that Chelsea are still keen on landing Lewandowski, and will do all they can to persuade him to move to Stamford Bridge.
The paper, who quote 'reports in France' as their source, say Chelsea had scouts at Dortmund's 2-1 win to take a look at Lewandowski, as well as Marseille's Florian Thauvin.
Chelsea have previously been linked with Lewandowski along with Manchester United, and are hoping that Dortmund will be willing to sell in January for a small fee rather than let him join their Bundesliga rivals for free in the summer.
The Blues look short of options in attack currently, with their three main strikers - Fernando Torres, Samuel Eto'o and Demba Ba - having only scored 11 goals between them in all competitions this season.
Despite their lack of firepower, Chelsea boss Jose Mourinho insists he won't delve into the transfer market in January for reinforcements.
The Express adds that scouts from Manchester City and Aston Villa were also at the game at the Stade Vélodrome last night.