It was suggested yesterday that the deal may have hit a snag after the French side demanded £18 million for the 19-year-old.
However RMC report that a €15 million fee has been agreed between Chelsea and the Ligue 1 outfit - and that the deal 'should' be completed soon.
RMC add that an agreement between the three parities - both clubs and the player - will be reached shortly and Zouma can be unveiled as a Chelsea player.
Previously the young defender has spoken out about his preference of a move to Chelsea, so talks should be a formality.
Chelsea have been active in the January window so far having already signed Nemanja Matic and Mohamed Salah, while selling Juan Mata to rivals Manchester United.
Yesterday, St Etienne co-president Roland Romeyer confirmed that more than one club aside from Chelsea were in the running for his signature.
"Some clubs have launched a bid for the player, but we will not change our strategy," he said.
“There have been discussions for Zouma with English, Italian and French clubs, but he will not be leaving this month unless we find an agreement with some of the potential buyers.
“If not, he will have to wait until the summer. We are under no obligation to sell.”
Manchester United are believed to have been interested in him previously.
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