Jose Mourinho has had the young defender on his transfer wishlist for some time, and is preparing a January bid.
But Arsene Wenger is also thinking of making an offer for the £12million rated defender, after receiving a glowing recommendation from trusted scout Gilles Grimandi.
Wenger is set to discuss January transfer targets this week, and Grimandi has told the Gunners boss to make a move for the France Under-21 star.
Chelsea hope they can fend off interest from the Premier League leaders in January, but there is the very realistic prospect of a bidding war developing.
Manchester City have also been linked with a move for Zouma, who is currently serving a lengthy ban for a horror tackle which broke an opponent’s leg.
In fact the defender is not set to return to action until February.
Arsenal remain desperate to strengthen their defence, despite the fact adding another striker remains the priority.
Wenger is aware that Thomas Vermaelen may request to leave in January as he remains third choice centre half behind Per Mertesacker and Laurent Koscielny, while Bacary Sagna is set to leave the club on a free transfer in the summer after refusing to sign a new contract.