The defender has gone to the London club for a medical with a deal being finalised later today for the 26-year-old.
It would seem that after Chelsea's third bid rejected by Everton, the blues boss decided to move his attention elsewhere for a short term replacement.
Winger Victor Moses, 24, is expected to sign a new contract at Stamford Bridge before joining West Ham on loan for the rest of the season.
While Djilobodji, only had a year left on his contract and made more than 160 appearances during his time at Nantes.
Mourinho has moved to address the Premier League champions' defensive concerns after they conceded nine goals in their first four league games.
That has left them eight points behind leaders Manchester City before they return to action at Everton on 12 September.