The Blues have added the Nerazzurri midfielder to their shortlist ahead of the January transfer window, but they face lots of competition.
Geoffrey Kondogbia looks set to leave Inter in January, with Chelsea "just one of many English clubs that are interested", Sportmasta understands.
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The 23-year-old is on Antonio Conte's transfer window shortlist, but Chelsea will look to sell players before buying, with players like Cesc Fabregas, John Obi Mikel and Branislav Ivanovic struggling for game time at Stamford Bridge.
At least five Premier League clubs have been monitoring Kondogbia, who became a bit-part player under former Inter manager Frank de Boer.
New coach Stefano Pioli hasn't offered any assurances to Kondogbia and Inter have begun steps to try to recoup as much, if not all, of the club-record £26.35 million fee they paid to Monaco in June 2015.
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Kondogbia is one of a host of other midfielders, including Roma's Radja Nainggolan, Fiorentina's Milan Badelj and Sevilla's Stephen N'Zonzi, on Chelsea's list as they look to add midfielders who can compete for places with Nemanja Matic and N'Golo Kante in Conte's two-man midfield.
The France international sees a move to the Premier League as a natural next step in a career which has become stunted since he arrived at the San Siro.
There is a belief that the Premier League suits his attributes and that a move to England can help him to regain his place in the France squad.
Meanwhile, Inter have expressed an interest in signing Oscar from Chelsea, but the Blues are reluctant to sell the Brazilian and still value him highly despite falling out of the starting line-up in recent weeks.