Zaha wants to remain in London and sees Chelsea as the ideal club to continue his resurgence.
If Willian indeed ends up parting ways with Chelsea this summer, Pedro will be the only recognised winger at Maurizio Sarri's disposal in addition to Hazard.
Palace's new contract offer would have seen Zaha's weekly wage rise from £100,000 to £125,000, but he wants to keep his options open.
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.
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Sarri also confirmed he would speak to Willian about a passport issue which has reportedly delayed his return. Chelsea manager Maurizio Sarri has expressed his annoyance at Willian's late return to pre-season training.
Opposition supporters mass in Zimbabwe capital in tense wait for election results
Millions of people voted peacefully on Monday in the first election since the army removed Robert Mugabe from power a year ago . European Union observers had earlier declared they found an "un-level playing field and lack of trust" in the election process.
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Several political parties have alleged vote-rigging, and have threatened nationwide protests , unless a new election is called. He has begun coalition talks to form the government after his party won 116 of 269 contested seats in the National Assembly.
Tottenham were interested in signing Zaha this window, but have made a decision to pursue Aston Villa's Jack Grealish instead.
There has certainly been more talk of outgoings at Chelsea this summer than incomings but with just a week until the transfer window closes, it looks as though the Blues will make a signing or two. Meanwhile, Tottenham are also weighing up a move for the player, although Palace are reportedly confident of keeping hold of him.
According to the Daily Mail, a potential swoop for Crystal Palace forward Wilfried Zaha will be at the top of the agenda.
The race to sign Zaha is getting increasingly unpredictable.
Palace will not sell the Ivory Coast global unless they are offered a huge sum to sell him for a second time in his career.