The 25-year-old would be open to a move to a top-six club and has told team-mates there is an offer for him to leave Selhurst Park.
Palace had offered the Ivorian global a new £125,000-a-week deal in a desperate attempt to keep hold of their Player of the Year, but it seems the bright lights of Stamford Bridge are too appealing for the 25-year-old.
The Ivory Coast global is adored by fans at Selhurst Park having played nearly 150 games for the club in two stints in south London.
Zaha who is one of Crystal Palace most influential player failed to join Everton when the switch fell through earlier in the summer.
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Tottenham were interested in signing Zaha this window, but have made a decision to pursue Aston Villa's Jack Grealish instead.
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Zaha wants to remain in London and sees Chelsea as the flawless club to continue his resurgence. While Hazard is expected to stay put, the Brazilian winger still faces an uncertain future, with Manchester United keen on signing him.
Blues boss Maurizio Sarri is now facing an attacking headache with Brazilian worldwide Willian set for a big money move to Manchester United or Barcelona, and Eden Hazard looking to force a move to Real Madrid. Zaha is thus, a viable target, who will bolster the Blues' attack irrespective of the Brazilian's departure.
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He clarified that it had nothing to do with football, but didn't rule out the possibility that he could be on the move before the transfer window closes on August 9.
But, according to Guardian Sport, Crystal Palace are determined that they will not sell Zaha. Meanwhile, Tottenham are also weighing up a move for the player, although Palace are reportedly confident of keeping hold of him.
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.
Chelsea appear to be winning the race for Crystal Palace's Wilfried Zaha.
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Despite Greipel's apology, Demare said he had used his comments as motivation. It didn't feel like a grab. "I think (he was) a bit of an idiot".