The Russian champions have reportedly offered £38 million for the Brazilian striker and are prepared to throw defender Bruno Alves into the mix in order to sweeten the deal.
Blues boss Roberto Di Matteo has made signing a forward his top priority this summer after losing Didier Drogba and Salomon Kalou earlier this summer but concedes his pursuit of Hulk is over.
Cavani is now the focus of his attentions with a Squeaky Bum Time source revealing the West London club have opened talks with the Serie A giants over a move.
Having struck 33 goals in 47 games last season Di Matteo believes he possess the correct physical attributes for Premier League target man and is hopeful of concluding a deal before the new season kicks off.
The Champions League winners’ hopes of landing Cavani were significantly boosted after his agent revealed in July that the Uruguay star is considering his future after his wife was mugged.
“It is not a good moment, but they are trying to get over it,” said Claudio Anellucci.
“She has left Naples to join Cavani. It is difficult to get used to the idea that these sort of things can happen to you.
“It is true that incidents of this type can happen to anybody, but the truth is they happen too often.”
Owner Aurelio De Laurentiis rates the 25-year-old at around £78m and has previously stated that he isn’t prepared to let him leave Naples on the cheap although it’s rumoured that he is willing to relent with his demands.
Having already splashed out over £80m on Eden Hazard, brother Thorgan, Marko Marin and latest recruit Oscar the Russian is ready to sanction one last big spend to boost an area he feels the club are deficient in.