The forward is being chased by the Blues, but Palace are unwilling to part with one of their most influential players.
A switch to Everton fell through earlier in the summer when Zaha decided he wanted to remain in London.
The Mirror, UK, is now reporting that Zaha has set his sights on a switch to Stamford Bridge, and has already told his fellow Eagles of his intentions.
Zaha informed the club he wants to leave, but Palace have replied only a massive offer will convince them to sell.
The 25-year-old is now weighing his options and could hand in a transfer request in an attempt to push through a move.
Palace offered Zaha a new-and-improved contract of £120,000 a week to stay at Selhurst.
Zaha wants to remain in London and sees Chelsea as the perfect club to continue his resurgence.
The Englishman’s failed spell at Manchester United prompted a return to Palace, but Zaha was vital in his side’s quest to avoid relegation last season.