Zaha, the 25-year-old former England worldwide who recently switched his allegiance to Ivory Coast, has been Palace's best performer since earning them a Premier League promotion back in 2013 and although the winger had a failed stint with Manchester United, his second spell at Selhurst Park helped the Eagles to retain top-flight status defying odds.
The forward is being chased by the Blues, but Palace are unwillingly to part with one of their most influential players.
Whether Chelsea move nearer to their valuation will depend on the future of Willian, who came close to joining Barcelona this summer and has also been linked with a move to Manchester United.
Further, it is reported that Zaha has rejected the club's advance at renewing his contract and bettering the package he now earns, with fresh terms giving him up to £125,000-a-week, a decent step-up from a recent contract he signed that sees him earn £100,000-a-week now.
The same report claims it would cost £70 million to prize Zaha away from Selhurst Park.
According to Mirror Sport, the Ivory Coast global has also reportedly told his Palace teammates of his plans, and would be willing to submit a transfer request should the club continue to price him out of a move.
Jorginho arrived from Napoli at the same time as Sarri while former England goalkeeper Rob Green was snapped up on a free transfer last month.
That gives Chelsea a clear run at the player, although significant hurdles remain if they are to agree a deal before the transfer window closes.