The Blues may make a move for the Italian before the close of the transfer window.
The Blues are keen to strengthen their defensive numbers before the end of the transfer window, with captain Phil Jagielka and John Stones their only current options at centre half.
Both Sylvain Distin and Antonlin Alcaraz were allowed to leave the club at the end of last season, meaning manager Roberto Martinez would have to rely on youth players Brendan Galloway or Tyias Browning at present.
That has led them to search for additional defensive cover, and they have sounded out Inter Milan over a potential move for Ranocchia according to Gianluca Di Marzio.
However, it seems a move for the Italian may only come about if defender John Stones leaves for Chelsea.
The Premier League champions have been in hot pursuit of the 21-year-old all summer, with a number of big bids for his services having been rejected outright by the Toffees, who are keen to keep hold of their prized asset.
And it is believed should they finally cave and decide to sell, which looks unlikely at this stage, then his move will create an almost immediate domino effect in the transfer market.