The Ivory Coast global has a special connection with Palace, having been at the club since he was nine years old, bar one forgettable season at Manchester United.
The Ivory Coast worldwide has been strongly linked with a move this summer and the Sun claims Chelsea are ready to launch an improved bid to sign Zaha after seeing their opening £30m plus Danny Drinkwater offer rejected.
Chelsea also have their eye on Zaha and the Blues want to force their way back into the Premier League's top four next season.
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. Zaha is thus, a viable target, who will bolster the Blues' attack irrespective of the Brazilian's departure.
Tottenham were interested in signing Zaha this window, but have made a decision to pursue Aston Villa's Jack Grealish instead.
But, Chelsea are hopeful of finally landing the 25-year-old with an improved offer worth £45 million, plus £15 million in add-ons and a massive sell-on fee.
The Crystal Palace winger has been heavily linked with a move away from Selhurst Park for a number of months after he seemingly single handedly ensured the Eagles' Premier League safety last term.