After missing much of the start to the season, Zaha has been instrumental since returning to action in mid-October.
Crucial goals against the likes of Chelsea, West Ham and Leicester have helped Palace climb to safety.
They are now unbeaten in seven Premier League matches, and the champions have taken notice of the Eagles’ talismanic attacker.
According to the Mirror, Chelsea are discussing whether to launch a bid for Zaha.
The Blues are keeping close tabs on the 25-year-old, who penned a new contract at Selhurst Park in the summer.
Hodgson has already acknowledged there is likely to be interest in Zaha from big clubs.
Tottenham were favourites to land Zaha but their pursuit faded after he penned fresh terms with Palace.
While Chelsea are now looking at the former Manchester United man, they could wait until the summer to move.
The Mirror adds Antonio Conte will be backed with funds in January and at the end of the campaign
Palace will be reluctant to lose Zaha next month as they are still in danger of being drawn into a relegation battle, sitting in 14th spot.
But the chance to prove himself again at a Champions League club like Chelsea may ultimately appeal to the Palace hero.
Arsenal have been linked with Zaha too.
But Starsport understands he is not on their agenda for January.