The Poland international had looked certain to join European champions Bayern Munich in the summer, while the player himself revealed earlier this month that he has already decided his next destination.
However, after enquiring about his services, Spanish giants Real Madrid were reportedly told that Lewandowski's representatives were in advanced negotiations with Chelsea.
The 25-year-old, who scored 36 goals in 49 matches for Dortmund last season - including four in the Champions League semi-final first leg against Real Madrid - could subsequently be headed to the Premier League instead.
Blues' boss Jose Mourinho was keen to sign a top-class striker in the summer, before eventually bringing in experienced Cameroon striker Samuel Eto'o on a one-year contract.
More recently, the Portuguese coach was seen watching the international friendly between Belgium and Colombia, with reports claiming he was there to watch AS Monaco's unsettled striker Radamel Falcao in action.
But Lewandowski would be considerably cheaper than Falcao - indeed he would be free if signed next summer - and perhaps a better fit for the Blues, too.