The French newspaper claims Chelsea, Inter Milan and Monaco are all keen to sign the teenage French under-21 international and have opened discussions with St Etienne regarding a deal.
But any agreement is unlikely to result in Zouma's transfer this month. More likely, the Frenchman would be allowed to leave at the end of the season.
Despite a 10-match ban for a reckless challenge that broke an opponent's leg this season, Zouma's rise through the club and international youth ranks to first-team has been seamless.
Earmarked as a future national team captain by Didier Deschamps, Zouma made his debut for St Etienne as a 17-year-old in 2011.
As a result of the suspension, he's made just 10 league starts for his club this season. But he's already viewed as an integral member of the first-team squad.
St Etienne's manager, Christophe Galtier, said recently: "I do not know if there has already been offers.
"I know these three clubs are watching Kurt very closely. Will they make offers? Anything is possible.
"The coach always wants to keep his good players."
Chelsea are expected to strengthen in the January transfer window, although Jose Mourinho recently said he is not looking to bring in another striker.
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