Zaha missed the opening weeks of the season with a knee injury but the 25-year-old has emerged as Palace's star man in recent weeks, with the Eagles putting together a seven-match unbeaten streak in the Premier League.
However, his form has started to attract the attention of the top-flight's biggest clubs and according to The Mirror, Chelsea are considering an offer for the start of 2018.
Head coach Antonio Conte failed to sign all of his transfer targets during the summer, and it has resulted in the Italian looking to strengthen his squad during the January window.
Palace are likely to reject interest in their attacker, but that may not stop the Blues from making an approach for a player who has scored four times in 12 appearances this season.
Zaha has previously been linked with Tottenham Hotspur, but it has been suggested that Spurs no longer regard the wideman as a priority target.