Zaha could have been seen as a direct replacement for Willian, the Brazil global has been heavily linked with a departure from Chelsea this summer.
But Mauricio Pochettino is now eyeing a move for Zaha, who is playing some of the best football of his career at the moment at Selhurst Park.
The Eagles are under little pressure to sell after tying Zaha to a long-term deal in 2017 worth £100,000 per week, but the Ivory Coast worldwide made his intentions clear by rejecting improved terms earlier this summer.
He has already snubbed interest from Everton as he is reluctant to move north again, after a failed stint with Manchester United.
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Tottenham have also been linked with Zaha, but are now trying to sign Aston Villa's Jack Grealish. The Blues though, have been more concrete with their interest in the 25-year-old.
According to the Sun, Chelsea were front-runners for Zaha as they would probably need a replacement for either Willian or Eden Hazard if the iconic duo leaves Stamford Bridge this season.
The Ivorian forward, who was a key figure for the Eagles last term, was reported to have told his teammates that he wants to move to Chelsea.
The race to sign Zaha is getting increasingly unpredictable.
This has left Chelsea with a clear run at Zaha and the newspaper says Palace will do business if they submit an offer close to their asking price before the transfer window slams shut on Thursday evening. An interesting next few days beckon.