The report suggests the Blues will make an attempt to secure the services of the winger in the summer, with Palace unlikely to consider selling their star asset in the New Year.
Arsenal have also been linked with a move for the £35m rated Ivorian, as a direct replacement for a recently-dwindling Alexis Sanchez - who is in the final year of his contract at the Emirates.
The 25-year-old has scored four goals in 12 Premier League appearances for the Eagles this season and looks to be in his best vein of form since joining England's top flight.
He has taken the lion's share of responsibility for sparking Roy Hodgson's attacking plays and has spearheaded a December surge from the bottom of the Premier League table to 14th.
The former Manchester United man has made himself a target for title and Champions League hopefuls this term, although he is currently tied to a five-year contract extension at Selhurst Park.
Chelsea are looking to further bolster their attacking options, in an attempt to close the 14 point gap to high-flying Manchester City atop the Premier League table. However, Antonio Conte's pursuit of the forward will not go unchallenged, as both Manchester City and Tottenham are believed to have made contact with his representatives last summer.
It seems potential suitors will have to wait until the summer window though, as Palace chairman Steve Parish revealed there is almost no chance of Zaha being sold in January last month:
"That's out of the question [Zaha leaving]," Parish told BBC's Match of the Day.
Crystal Palace Star Wilfried Zaha's Performance Leaves Spurs Fans Purring on Twitter https://t.co/lhexl20VXD— Crystal Palace Pro (@CPFCpro) December 17, 2017
"We need to keep going, make sure we get as high as we can up this league.
"He's a joy to work with for every manager and obviously he makes a big difference to us on the pitch."