The 25-year-old has now rediscovered his best form and was the talisman for the Eagles the last term scoring nine goals and notching up five assists as well.
But the Mirror suggest that the Ivory Coast global has rejected a fresh extension that would improve his terms even further to £125,000-a-week.
And if Chelsea come in with a mammoth bid nearing Palace's demands, then they will reluctantly do business.
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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That is unlikely to change whether or not Chelsea make a move to sign him before Thursday's deadline as they have so far been unwilling to offer more than £30m plus players on loan.
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.
"I spoke to Wilf yesterday and he certainly gave me no indication it was true about wanting to quit the club", Hodgson told talkSPORT.
Speaking on The Alan Brazil Sports Breakfast, Allardyce said: "I think the experience of Manchester United and then coming back to Palace re-established him as a top player".