The report claims Jose Mourinho's side have reached an agreement with the player's representatives to bring Zouma to Stamford Bridge but he may not link up with Chelsea until the summer.
The Blues have been extremely busy this January window, offloading Juan Mata and Kevin de Bruyne for a combined £53m while Nemanja Matic has come in from Benfica and Mohamed Salah from Basel.
Southampton defender Luke Shaw remains a target for Mourinho's team, but the report suggests they're much closer to landing Zouma.
A fee in the region of £10m is thought to be the amount required to encourage St Etienne to part with Zouma.
The 19-year-old French starlet has already been tipped for the very top by many in France, including France national team boss Didier Deschamps.
A move for Zouma would continue Chelsea's shift to bringing in the world's best young players. Mourinho has spoken about signing younger players to work on the squad's evolution.
And Zouma, still a teenager, would be viewed as a potential long-term replacement for John Terry.