The winger had already rejected a move to Everton earlier this summer, appearing reluctant to move back north after a troubled spell with Manchester United which saw him loaned out three times in two years.
Blues boss Maurizio Sarri is now facing an attacking headache with Brazilian global Willian set for a big money move to Manchester United or Barcelona, and Eden Hazard looking to force a move to Real Madrid.
Despite reports to the contrary, Tottenham have not registered an interest in Zaha so far this summer, with Mauricio Pochettino instead focusing his efforts and limited resources on Aston Villa midfielder Jack Grealish.
A five-year contract extension last year tied him up to the summer of 2022, but a huge bid is tipped to be enough to lure Zaha in and the Blues, struggling to retain their stars as well as failing to land preferred transfer targets in absence of Champions League football, will have a significant boost if they manage to strike a deal before the new Premier League season kicks off next weekend.
The Blues, who finished fifth in the top-flight last term, have signed only Jorginho and Rob Green this summer but have expressed interest in Palace's Zaha.
That deal would have increased his wage to £125,000 per week, but Zaha is well aware that he could earn significantly more at Stamford Bridge.
After a fantastic 2017/18 season for Crystal Palace, Wilfried Zaha is a man in demand.
Shockingly though, Zaha has told his teammates that there is "an offer for him to leave Selhurst Park", which reads as a major blow to Palace supporters.