But they are refusing to be dragged into an expensive bidding war for a striker they deem to be overpriced.
Both Real Madrid and Manchester City have been linked with Cavani, and Chelsea fear the forward's price will be driven excessively high by the interest.
They remain keen on the Uruguayan international, but will now actively explore alternatives and are set to turn to Lewandowski. The report claims Fiorentina's Stevan Jovetic and Manchester City's Edin Dzeko have both been considered by the Stamford Bridge hierarchy, but Borussia Dortmund's steadfast refusal to sell Lewandowski to Bayern Munich has piqued Chelsea's interest.
The club now feels it stands a good chance of signing one of Europe's top strikers for half the price of Cavani.
Lewandowski has just 12 months remaining on his Dortmund contract, and the report claims the Champions League finalists would take £25m for him this summer.
Manchester United have invested much time and effort into their pursuit of the Polish international, but Chelsea feel they could steal a march on their Premier League title rivals after United's interest cooled in recent weeks.
Jose Mourinho is keen to strengthen his attacking options, and has clinched his first signing of the summer already - the £20m capture of Germany forward Andre Schurrle from Bayer Leverkusen was announced earlier this week.