Ranocchia has seen his first team opportunities limited at the San Siro, and manager Walter Mazzarri is reportedly ready to cash in on the defender in January.
Reports in Italy suggest Jose Mourinho is hoping to persuade the 25-year-old to make the switch to Stamford Bridge as he prepares for life without David Luiz.
The Brazilian has been consistently linked with a move away from Chelsea, with Barcelona thought to be preparing a January bid for his services.
Ranocchia had previously claimed he was committed to the Inter cause, but he is yet to sign a new contract with the Serie A giants.
His stalling over a new deal is said to have angered Inter officials, who are now happy to let the centre back leave the club.
Arsenal, Tottenham and Manchester United are all thought to be keen on the Italian, but Chelsea are understood to be in pole position to complete the deal.
Ranocchia and Luiz are both looking for first team football ahead of next summer’s World Cup, and a move that would see both given regular first team football is thought to be appealing.