The 18-year-old centre-back, who currently plies his trade for Ligue 1 outfit Saint Etienne, has been tipped as a star of the future in his homeland, and is attracting admiring glances from a number of potential suitors.
Red Devils boss Sir Alex Ferguson is keen to bring Zouma to Old Trafford, as he continues his search for a long-term replacement for crocked captain Nemanja Vidic.
The Serbian stopper has struggled to maintain his fitness over the past 12 months, after suffering two serious knee injuries.
Vidic suffered his first injury when rupturing a cruciate knee ligament in a Champions League group game at Basel in December 2011, which kept him out for the remainder of that season. He then required surgery to the meniscus in the same right knee after experiencing the problem during training with the club back in September.
Manchester United have also sent scouts to watch Benfica defender Ezequiel Garay on several occasions this season, but Ferguson is now keeping a close eye on Zouma.
Valued at around £8million, the Frenchman might prove to be a more viable option for the Premier League leaders, despite the fact Zouma has been offered a new contract by St Etienne.
Expect United to step up their interest and try to secure his signature in the summer.